Land-surface phenologies from AVHRR using the discrete fourier transform

Transcription

1 Remote Sensing of Environment 75 (2001) 305± Land-surface phenologies from AVHRR using the discrete fourier transform Aaron Moody*, David M. Johnson Department of Geography, University of North Carolina at Chapel Hill, Chapel Hill, NC USA Received 3 August 1999; accepted 7 August 2000 Abstract The first and second harmonics of the discrete Fourier transform (DFT) concisely summarize the amplitude and phase of annual and biannual signals embedded in time-series of Advanced Very High Resolution Radiometer (AVHRR) Normalized Difference Vegetation Index (NDVI) data. We applied and evaluated the DFT using monthly composited NDVI data over a 7-year period for a km study area in southern California. The study area contains strong gradients in environmental conditions and basic vegetation formations. Analysis of the DFT harmonics for six point-locations provided a basis for linking the DFT results to basic vegetation types according their characteristic phenologies. The mean NDVI, or 0th-order harmonic, indicated overall productivity, allowing the differentiation of unproductive, moderately productive, and highly productive sites. The amplitude of the first harmonic indicated the variability of productivity over the year as expressed in a single annual pulse of net primary production. This summarized the relative dominance of evergreen vs. deciduous or annual habit. The phase of the first harmonic summarized the timing of green-up relative to the timing of winter and spring rains. This differentiated rapidly responding annual grasslands, slowly responding evergreen life-forms, and irrigated agriculture. The second harmonic indicated the strength and timing of any biannual signal. This provided information on secondary vegetation types, such as subcanopy grasses beneath evergreen woodlands or mixtures of annual grasslands and irrigated agriculture. The point-based analysis provided the foundation for a regional analysis of the entire study area. The mean NDVI and first- and second-order amplitude and phase, in conjunction with 148 fieldsampled polygons, were used to produce an unsupervised classification of basic vegetation formations for the study area. These results were evaluated by comparison with other land cover products, and through assessment using field-sampled test regions. D 2001 Elsevier Science Inc. All rights reserved. 1. Introduction The characterization of vegetation phenologies at regional, continental, and global scales can provide support for several primary Earth science initiatives. For example, intraannual variability in terrestrial plant productivity is a key driver of dynamics in surface-atmosphere fluxes of carbon, energy, and moisture, and plays a critical role in other biogeochemical cycles as well (Sellers et al., 1994; Tucker, Townshend, & Goff, 1985a). Surface phenologies can also provide baseline data from which to monitor changes in vegetation associated with events such as fire, drought, land use conversions, climate fluctuations, and directional climate change (Justice, Holben, & Gwynne, 1986). Phenologies, as expressed in pixel time trajectories, can also be * Corresponding author. address: aaronm@ .unc.edu (A. Moody). used as a basis to partition surface cover into functional vegetation types (Loveland, Merchant, Ohlen, & Brown, 1991; Tucker et al., 1985a). We present a Fourier-based method for characterizing baseline intra-annual variability in vegetation productivity. The analysis is based on a 7-year (1990±1996) time series of biweekly composited Normalized Difference Vegetation Index (NDVI) data from the Advanced Very High Resolution Radiometer (AVHRR) (Eidenshink, 1992). The study, a km area in southern California region, contains strong gradients in vegetation type that follow gradients in temperature and precipitation regimes associated with coastal proximity, elevation, and physiography (Holland & Keil, 1995; Smith, 1998). Evaluation of the methodology consists of three components. First, we analyze amplitude and phase data from the first and second harmonics of the Fourier transform with respect to known surface characteristics at six point locations distributed throughout the study area. Second, these /00/$ ± see front matter D 2001 Elsevier Science Inc. All rights reserved. PII: S (00)

2 306 A. Moody, D.M. Johnson / Remote Sensing of Environment 75 (2001) 305±323 same derived variables are mapped over the study area and assessed with respect to the distribution of functional vegetation types within mean-phase-amplitude space. Third, the separation of vegetation types into different regions of mean-phase-amplitude space in the first and second harmonics is used as a means to classify vegetation into six basic types with different characteristic phenologies. The classification is evaluated through an intercomparison with other AVHRR-based land cover products and validated using field data from the study region. There are several valuable properties associated with the use of Fourier analysis to analyze vegetation phenology. Discrete Fourier Analysis is an objective, consistent, and concise summarization of the temporal signature that is sensitive to systematic changes in vegetation but relatively insensitive to nonsystematic data noise. In addition, the higher order harmonics of the Fourier decomposition may capture the phenology of secondary vegetation components or rapid surface changes associated with discrete-event disturbances such as fire, deforestation, or flooding. 2. Background Since the 1980s vegetation phenology has been studied over broad scales using time series of AVHRR data (Duchemin, Goubier, & Courrier, 1999; Justice, Townshend, Holben, & Tucker, 1985; Townshend, Justice, Li, Gurney, & Mcmanus, 1990). Some of this work has focused on producing characteristic phenologies and monitoring surface dynamics to evaluate inter- and intra-annual deviations from baseline conditions (Duchemin et al., 1999; Townshend & Justice, 1986; Justice et al., 1985, 1986; Lambin & Strahler, 1994; Malingreau, Tucker, & LaPorte, 1989; Moulin, Kergoat, Viovy & Dedieu, 1997; Reed et al., 1994). These analyses can provide a basis for monitoring fluctuations and directional trends in surface characteristics as driven by interannual climate variability, climate change, and other natural and anthropogenic effects that impact the functioning of ecosystems and agricultural regions. Considerable effort is also devoted to deriving biophysical characteristics to provide land surface parameters for physically based models of climate, hydrology, net primary productivity, and biogeochemical cycles (Sellers et al., 1994; Spanner, Pierce, Running, & Peterson, 1990; Tucker, Fung, Keeling, & Gammon, 1986; Tucker & Sellers, 1986; Tucker, Vanpraet, Sharman & Ittersum, 1985b). However, some surface parameters are difficult or impractical to estimate directly. In this case, parameter distributions can be assigned according to functional vegetation formations provided by land cover classifications (Townshend, Justice, Li, Gurney, & McManus, 1991). The temporal profile of NDVI provides a basis for discriminating land cover classes based on their phenology (DeFries et al., 1995; DeFries & Townshend, 1994; Loveland et al., 1991; Townshend, Justice, & Kalb, 1987; Tucker et al., 1985a). For example, Townshend et al. (1987) applied supervised maximum likelihood to classify South American land cover types using multitemporal composited NDVI data from AVHRR. Townshend et al. (1987) and Tucker et al. (1985a) used boundaries around characteristic phenologies as transformed into principle components space to differentiate basic vegetation classes for Africa and South America, respectively. Lloyd (1990) and Running, Loveland, Pierce, Nemani, and Hunt (1995) employed binary decision trees to classify vegetation based on summary indices derived from time series of AVHRR-NDVI data. Such indices, or phytophenological variables, can include the mean NDVI, maximum NDVI, annually integrated NDVI, date of the maximum NDVI, length of the growing season, or rate of senescence. Similar analyses have also included temporal patterns in surface temperature (Nemani & Running, 1997). Loveland et al. (1991) used 1 year of 1-km, monthly composited AVHRR-NDVI data to generate an unsupervised classification for the conterminous United States. Clusters were stratified based on ancillary environmental data and were used to identify 159 land cover classes. Other efforts have used classification trees (Friedl & Brodley, 1997; Hansen, Dubayah, & DeFries, 1996) or neural networks (Gopal, Sklarew, & Lambin, 1994) applied to time series of NDVI data, or to derived indices. For example, Friedl et al. (2000) used a decision tree classifier to produce a 1-km class map of land cover for North America with 17 basic classes. In addition to these classification studies, bioclimatological analyses have illuminated connections between dynamics of vegetation phenology and climate variables such as precipitation and temperature (Goward, 1989; Rundquist, Harrington, & Goodin, 2000; Tucker et al., 1985a; Yang, Wylie, Tieszen & Reed, 1998). These signals may respond to long-term climate change, as well as climatic anomalies such as El NinÄo/Southern Oscillation (Malingreau, 1986). Little literature exists on the use of temporal Fourier analysis to analyze AVHRR data. Most of this work is restricted to short contributions. Olsson and Eklundh (1994) and Verhoef, Menenti, and Azzali (1996) used Fourier analysis to evaluate land surface dynamics using monthly mean Global Vegetation Index data for South America and Africa, respectively. Menenti, Azzali, Verhoef, and Van Swol (1993) mapped agroecological zones using a Fourier transform of AVHRR-NDVI time series. Andres, Salas, and Skole (1994) applied Fourier analysis to spatially aggregated AVHRR data and found that the Fourier harmonics are sensitive to seasonal variability in vegetation productivity. Rogers, Hay, and Packer (1996) used Fourier analysis of variables derived from AVHRR data to predict the distribution of Tsetse fly in West Africa. Finally, Azzali and Menenti (2000) described the use of Fourier analysis for producing a bioclimatological regionalization of southern Africa. In this work we present a full treatment of the use of

3 A. Moody, D.M. Johnson / Remote Sensing of Environment 75 (2001) 305± Fourier analysis for assessing vegetation dynamics and classifying basic vegetation formations. We also provide a careful evaluation of these approaches over an area for which we have a thorough understanding of the vegetation and climate characteristics. 3. Methods 3.1. Discrete Fourier transform Decomposition of temporal data to the frequency domain can be achieved using Fourier analysis, by which frequency information is represented as constituent sine and cosine functions (Briggs & Hensen, 1995). Signals that are thus spectrally decomposed can be converted back to the temporal domain via an inverse Fourier transform. If the original data is discrete rather than continuous, then the discrete Fourier transform (DFT) is used. The DFT requires a regular spacing of samples within the temporal domain, and the data sampling rate must be at least double the rate of the frequency of interest embedded in the signal. The maximum frequency resolved by the DFT is the Nyquist frequency, given by Eq. (1): f Nyquist ˆ V 1 2 where V is the highest frequency signal within the data. The discrete Fourier transform is given by Eq. (2): y k ˆ 1 N XN 1 c k e i2k =N kˆ0 2 where N is the number of samples in the time series, k is an index representing the current sample number, i is an imaginary number, and c is the kth sample value. The DFT formula decomposes into a set of trigonometric forms through the use of Euler's equation [see Eq. (3)]: e i ˆ cos isin 3 where is an angular term between 0 and 2 radians. Substituting Euler's equation into the DFT expression and expanding gives Eq. (4): 2n y n ˆ a 0 a 1 cos b 1 sin 2n N N 4n a 2 cos b 2 sin 4n... N N 2kn a k cos b k sin 2kn : 4 N N Here, a 0 is the mean, a 1 and b 1 are first-order trigonometrics, a 2 and b 2 are second-order trigonometrics, and so on to the kth order. Each order represents a harmonic where the 2p expressions relate to the first harmonic, the 4p expressions relate to the second harmonic, and so on to the kth harmonic (Briggs & Hensen, 1995). The resulting y is a complex number with a real and an imaginary component, but can be described in polar form as shown in Eq. (5) and Eq. (6): 1=2 y magnitude ˆ y 2 real y2 imaginary 5 y phase ˆ tan y imaginary : 6 y real The Fourier analysis of multitemporal NDVI data presented in the following sections is based on a monthly sampling rate. The real and imaginary components of the Fourier transfer are described as amplitude and phase, represented in units of NDVI and month, respectively. Although six harmonics are produced by the DFT, only the amplitude and phase of the first two harmonics are considered Study area The study region is a km area in southern California containing much of the southern part of the Los Padres National Forest (Fig. 1). This area exhibits a range of topographic and climatic conditions with associated variations in vegetation. The study area was chosen for two reasons. First, it is large enough to encompass broad gradients in vegetation formations that are appropriate for mapping using AVHRR data. Second, the area resides within a single macroclimatic regime and is sufficiently small and accessible to be well sampled and understood through field-based study. The study area has a Mediterranean-type climate with cool, wet winters, and warm, dry summers (Barbour & Major, 1977; Smith, 1998). Most precipitation occurs between December and April as a result of Pacific storm tracks that form during the winter. The ocean moderates the daily high and low temperatures near the coast, and coastal fog is common from June to September (Holland & Keil, 1995). Temperature extremes increase and precipitation decreases with distance from the coast. Conditions throughout the region become cooler and moister with elevation above about 500 m. The basic vegetation formations include evergreen sclerophyllous shrublands (chaparral), evergreen broadleaf savanna and forest, semidesert scrub, annual grasslands, needleleaf savanna and forests, and mixed needleleaf/broadleaf savanna and forest (Holland & Keil, 1995; Smith, 1998). Savanna density ranges from open to woody with large to dwarfed tree stature and grass and/or shrub understory. Shrublands range from large stature, closed canopy chaparral to sparse scrub, sometimes with a thin grass understory. Annual grasslands can range from tall and dense to short and sparse. Open semidesert scrub and sparse grasslands may be nearly barren. Deciduous tree species

4 308 A. Moody, D.M. Johnson / Remote Sensing of Environment 75 (2001) 305±323 Fig. 1. Landsat TM image composite from May Major features are identified to provide reference for discussion of results. Points 1 through 6 represent the six point locations used for part of the analysis. These are Buttonwillow (1), Salsipuedes (2), New Cuyama (3), Big Pine Mountain (4), Dry Canyon (5), and Pozo Summit (6). occur in dense stands where perennial streamflow supports riparian corridors. The general trend toward drier conditions with increasing distance from the coast is modulated by a roughly parallel series of northwest± southeast trending mountain ranges and intervening valleys (Fig. 1). Middle to upper elevations in the more marine-influenced mountains (Santa Ynez, San Rafael, Sierra Madre, and La Panza Ranges) support coastal sage scrub, closed canopy chaparral, and evergreen forest and woodlands. Open to closed oak woodlands can occur at all but the highest elevations in these areas, generally becoming denser and smaller in stature with increasing elevation. Conifer/oak woodlands occur at upper elevations and transition to montane coniferous forests on the highest mountains (e.g., Big Pine Mountain, Mount Pinos). Valleys and foothills near the coast support oak woodlands, grasslands, and agriculture. Interior, dry mountainous regions (Caliente and Temblor Ranges) support mainly open formations, including Oak-Juniper-Pinyon Woodlands, open chaparral or semidesert scrub, and grasslands, although these mountains can

5 A. Moody, D.M. Johnson / Remote Sensing of Environment 75 (2001) 305± support closed canopies at higher elevations. Arid interior valleys and foothills are dominated by grassland and open semidesert scrub unless irrigated for agriculture. Vast grassland areas in the foothills of interior mountain ranges provide open range for cattle. The broader interior valleys (e.g., San Joaquin Valley) are used for irrigated agriculture to produce a wide diversity of crop types, including grapes, cotton, almonds, citrus, broccoli, strawberries, lettuce, avocados, nursery and Christmas trees, and ornamental flowers (California Department of Food and Agriculture, 1996). The most significant land cover conversion process is urbanization, especially near the larger cities of Santa Barbara, San Luis Obispo, and Santa Maria. Much of the annual grasslands, coastal sage scrub, and oak woodlands near the coast have been replaced by suburban development. In Fig. 1, red and purple areas can be generally interpreted as annual grasslands, open shrublands, fallow agricultural fields, and urban areas. White pixels are dry, open washes and other sparsely vegetated areas. Dark green pixels represent dense vegetation such as closed canopy chaparral, dense woodlands, conifer forest, and evergreen broadleaf forest. Agricultural fields are obvious from their geometric shape and appear dark green, bright green, dark purple, or light purple, depending on field and crop status. 4. Analysis This analysis is based on a set of 149 biweekly composited AVHRR-NDVI images of the conterminous U.S. produced by EROS Data Center (EDC) (Eidenshink, 1992). These are 1-km 2 spatial resolution data that span the period from March 1990 to December The literature contains numerous descriptions of AVHRR data (Goward, Markham, Dye, Dulaney, & Yang, 1991), NDVI (Goward et al., 1991), compositing of AVHRR NDVI data (Holben, 1986), and the EDC Conterminous U.S.A. data product (Eidenshink, 1992). The reader is referred to these sources for background on the data. A pixel region corresponding to the study area was windowed from the composited AVHRR-NDVI data and georeferenced to a Landsat Thematic Mapper (TM) scene from May The 7 years of biweekly composited AVHRR-NDVI data were averaged on a monthly basis to produce a 12-band data set that represents monthly NDVI data for an average year. A set of 148 land cover polygons were sampled in the field in 1997 and were spatially referenced to the satellite data set. These were used to label unsupervised clusters in the land cover classification described below. An additional set of 28 large polygons, sampled in the field in 1999 and digitized onto Landsat TM data, were used to validate the land cover map. The DFT was applied to the AVHRR data set on a per pixel basis for the entire study area. The higher-order harmonics (three, four, five, and six) were discarded because they had trivial amplitudes, and there was no logical reason to anticipate trimodal or higher-order signals in this environment. We first evaluated the DFT results for a set of six point locations within the study region (Fig. 1, Table 1). The selection criteria for these locations were that each point should represent a unique bioclimatological setting within a large homogeneous region of vegetation. Monthly precipitation data was available from cooperative climate stations at three of these sites (NOAA/NCDC, 1998). The site-based analysis provided a general understanding of the DFT and how it relates to the range of bioclimatological scenarios that characterize the study area. The analysis for the six Table 1 Amplitude and Phase Values for the First Two Harmonics of the Discrete Fourier Transform for the Six Focus Sites Site Mean Amp. I Phase I Amp. II Phase II Site Characteristics 1. Buttonwillow :8 Dry interior valley: irrigated annual crops, fallow fields, and some grassland 2. Salsipuedes :10 Coastal foothills: woodland, grassland, chaparral, small agricultural fields. 3. New Cuyama :9 Interior valley: grassland, semidesert scrub, some irrigated agriculture 4. Big Pine Mountain High elevation: conifer or mixed evergreen woodland/forest 5. Dry Canyon Dry interior lower mountains, open semidesert scrub, sparse annual grassland 6. Pozo Summit High-elevation interior: closed canopy chaparral, oak-conifer woodland A general description of the physiographic setting and vegetation formations surrounding each site are provided. Units for the mean and amplitude values

6 310 A. Moody, D.M. Johnson / Remote Sensing of Environment 75 (2001) 305±323 point locations was followed by a regional analysis of the DFT for the entire study area, as well as an assessment of the DFT as a basis for discriminating basic functional vegetation formations. The classification was produced using the ISODATA clustering algorithm (Richards & Jia, 1999). Thirty clusters were produced and merged to a set of six basic vegetation formations: Evergreen, Grassland, Irrigated Agriculture, Sparse/Barren, and two Savanna classes. These classes are more fully described below. Cluster merging and labeling was based on the set of 148 reference polygons. The polygons were originally characterized according to a 17- class land cover taxonomy used by the International Geosphere-Biosphere Program (IGBP). For this analysis these classes were collapsed to the six basic vegetation formations. The results of the land cover classification were evaluated in three ways. First, they were compared with data from the Land-Cover Characteristics Database for the Conterminous U.S. produced at EDC (Loveland et al., 1991). Seventy-nine of the 159 classes in the EDC data set were labeled as present in the study area. These were crosswalked into the six classes used in our analysis by combining all irrigated agricultural classes, all evergreen shrub and forest classes, all grassland classes, all semidesert scrub classes, and all woodland classes. Second, we compared the Fourierbased land cover classification with a 1-km land cover product of North America produced at Boston University (BU) (Friedl et al., 2000). The BU product follows the IGBP classification, which was collapsed to correspond with our classification scheme. Comparison with the EDC and BU products involved georeferencing the land cover data sets, crosswalking the classifications, evaluating classwise and overall correspondences, and evaluating difference images between the three products. There are several general problems associated with the comparison of different class maps that will be discussed below. In addition to the map comparisons, we also evaluated all three maps using a set of 28 validation regions that were identified in the field in August 1999 and digitized onto a 1997 Landsat TM scene. These polygons were labeled according to the classes used in this analysis. Since the test polygons each had to contain numerous AVHRR pixels, they were only selected for areas that consisted of a broad expanse of the given class type. These data were georeferenced and resampled to coincide spatially with the AVHRR data set. 5. Results and assessment 5.1. Specific sites Buttonwillow Site 1, near the town of Buttonwillow, is an interior location within a large, irrigated agricultural area at the edge of the San Joaquin Valley (Fig. 1). This site has a moderate mean annual NDVI (0.3). The first-order harmonic captures most of the temporal variability in NDVI at Buttonwillow, expressing a strong seasonality, or amplitude (0.22), which is typical for irrigated annual crops (Fig. 2, Table 1). The phase (timing of the peak) is near sample seven, indicating a maximum NDVI in July. This is substantially out of phase with the rainy season (Fig. 2) and coincides with the full emergence of irrigated crops. Under normal conditions, this dry interior valley would green up during the rainy season due to the rapid emergence of annual grasses and other herbaceous annuals in response to available moisture. This signal, although subdued, is still expressed at this site due to remaining grassland areas and fallow fields. It is characterized by the second harmonic (dashed sinusoidal line in Fig. 2), or biannual sine-wave response, which peaks once in late winter/early spring (the end of the rainy season) and again during crop maturity. When the NDVI is at its highest during the summer, the first- and second-order harmonics are in phase and combine to produce a large peak. During the winter they are out of phase, but the NDVI is slightly elevated as expressed in the second harmonic, possibly due to grasses that respond quickly to precipitation. Nevertheless, the amplitude of the second harmonic (0.05) is small relative to the first harmonic. The addition of the first- and second-order harmonics (dotted curve in Fig. 2) closely follows the original time series (vertical lines). This confirms that little signal remains in the last four harmonics for this site, as is the case with all six sites Salsipuedes The second site is located at the Salsipuedes Canyon gauging station situated in a lower-elevation mountainous coastal area situated between Point Conception and Point Arguello (Fig. 1). This site receives abundant precipitation relative to Buttonwillow (Fig. 3b). The mean NDVI is moderately high (0.33), indicative of the evergreen canopy of oak woodlands and chaparral that occupy this area. The subdued amplitude of the first harmonic (0.15) (Fig. 3, Table 1) reflects the presence of evergreen cover that does not fluctuate significantly throughout the year. The moderate temporal signal that does occur is in response to the emergence of understory grasses and new shoot production in the chaparral and oak woodlands. The phase, or timing of the peak NDVI, is during late April to early May, and the productivity phase for this area extends through July. These characteristics reflect the delayed response of woody evergreen vegetation to winter precipitation relative to the rapid response of annual grasses (Figs. 3a and 3b). The second harmonic peaks in late March, slightly earlier than the first harmonic, and again in late September. Although the amplitude is small relative to the first harmonic (0.05), the March pulse indicates the more rapid emergence of understory grasses in response to winter and spring rainfall. The September pulse may correspond to maturing

7 A. Moody, D.M. Johnson / Remote Sensing of Environment 75 (2001) 305± Fig. 2. Discrete Fourier Transform decomposition for Buttonwillow (a) and monthly average precipitation data (b). The vertical lines in (a) represent average NDVI values for each month. The peak NDVI and the peak precipitation are about half a wavelength out of phase, indicative of irrigated agriculture. irrigated field crops that are cultivated in narrow valley areas near Salsipuedes New Cuyama The third site, New Cuyama, contains a mix of annual grassland, open shrub, and irrigated agriculture (Fig. 1). Although not as arid as areas further to the northeast, New Cuyama is fairly dry and can receive some late summer convective rainfall (Fig. 4b). The first harmonic for New Cuyama has an amplitude of only 0.05 around a relatively low mean value of 0.23 (Fig. 4, Table 1). The phase of the first harmonic (early April) reflects the rapid emergence of the annual grasses in this area following winter and early spring rains (Fig. 4b). The second harmonic has an equally large amplitude and is shifted roughly 1 month earlier than the first harmonic, peaking in March, and again in September (Fig. 4, Table 1). The springtime peaks of the first two harmonics combine to emphasize the strength of grassland emergence in response to the rainy season. However, a strong bimodal phenology is also indicated by the equal amplitudes of the first two harmonics (Fig. 4, Table 1). In late summer to early fall, the first harmonic reaches its minimum, while the second harmonic approaches a maximum (Fig. 4). The result is a slight pulse in overall productivity, reflecting the maturity of irrigated late season crops in the Cuyama Valley Big Pine Mountain Big Pine Mountain (Site 4, 2,081 m) represents highelevation sites in the region and supports conifer forest and woodland (Fig. 1). Big Pine Mountain has the largest mean NDVI of the six study sites (0.43), indicating the large

8 312 A. Moody, D.M. Johnson / Remote Sensing of Environment 75 (2001) 305±323 Fig. 3. Discrete Fourier Transform for Salsipuedes (a) and monthly average precipitation data (b). The peak NDVI closely follows the peak precipitation. volume of green biomass that persists throughout the year. The small amplitude of the first harmonic (0.05) (Fig. 5, Table 1) reflects the subdued phenological signal of the dense evergreen vegetation. The phase of the first harmonic occurs in late June to early July, indicating the delayed production of new shoot biomass in the high-elevation conifer forests and subcanopy shrubs at this site. Winter precipitation often falls as snow, contributing to the delay of biomass productivity until after snowmelt. There is almost no signal in the second-order harmonic Dry Canyon Dry Canyon (Site 5) is in the rain shadow of the San Rafael Mountains and receives little precipitation (Fig. 1). The area supports sparse grasslands and semidesert scrub. The mean NDVI at Dry Canyon (0.21) is the lowest of the six sites. The amplitudes of the first two harmonics are nearly zero (Fig. 6, Table 1). The sparse, open shrublands at Dry Canyon exhibit slight increases in NDVI during late winter Pozo Summit Pozo Summit (Site 6) consists of closed canopy chaparral, dense oak woodland, and conifer woodlands (Fig. 1). These vegetation formations are similar in function to the Big Pine Mountain site. The first-order harmonic for this site peaks during May with a moderate amplitude of 0.10 around a mean value of 0.30 (Fig. 7, Table 1). The secondorder harmonic is trivial. Although Pozo Summit is also vegetated with dense evergreen vegetation, the mean NDVI is lower than Big Pine Mountain, and the phase is shifted

9 A. Moody, D.M. Johnson / Remote Sensing of Environment 75 (2001) 305± Fig. 4. Discrete Fourier Transform for New Cuyama (a), and monthly average precipitation data (b). The peak NDVI is in phase with the peak precipitation. The first and second harmonics have roughly equal amplitude. There is some summer precipitation at this site, probably reflecting summertime convective storms in the interior. Fig. 5. Discrete Fourier Transform for Big Pine Mountain. This site has a high NDVI and almost no signal from the second harmonic. Fig. 6. Discrete Fourier Transform for Dry Canyon. This site has a low NDVI and very little intra-annual dynamic.

10 314 A. Moody, D.M. Johnson / Remote Sensing of Environment 75 (2001) 305±323 Fig. 7. Discrete Fourier Transform for Pozo Summit. This site is similar to Big Pine Mountain, with a slightly earlier peak. back about 1 month to May. The first harmonic reflects a springtime pulse of new shoot growth in response to winter and spring rains. The woody vegetation at Pozo Summit responds more slowly than annual grasses to winter precipitation, with a concomitant shift of the peak NDVI later in the season than the grassland sites (e.g., compare Figs. 4 and 7) Regional assessment The magnitude and phase of the first two harmonics are mapped across the study area to support a regional assessment of phenology (Figs. 8 and 9). The six sites discussed above provide a reference to support the interpretation of these data. The region with the greatest first-order amplitude (Fig. 8a) is the large agricultural area surrounding Buttonwillow (Site 1), located along irrigation sources in the San Joaquin Valley. Irrigated agriculture produces variability in NDVI of 0.25 around the mean. The coastal region with evergreen chaparral and woodland vegetation near Salsipuedes (Site 2) has moderately high variability with amplitudes up to Areas associated with the more temperate mountain ranges (Santa Ynez, San Rafael, Santa Lucia, Sierra Madre) are vegetated primarily by closed chaparral, dense oak woodland, or conifer woodland/forest (e.g., Big Pine Mountain and Pozo Summit). These evergreen life-forms exhibit little intra-annual variability in NDVI (Fig. 8). The intermediate foothills and valleys, as well as the drier interior mountains (Caliente and Temblor Ranges), support seasonal grasslands that express greater variability throughout the year due to their annual habit and rapid response to annual precipitation. The region surrounding Dry Canyon (Site 5) and the interior nonagricultural valley areas just southwest of the San Joaquin Valley have sparse vegetation, exhibiting almost no variability around low mean NDVI values. The region of greatest variability in the second harmonic (Fig. 8b) is within the San Joaquin Valley, suggesting the presence of either biannual crops or a combination of irrigated crops that peak in midsummer, and nonirrigated fallow fields with annual grasses that peak in late winter/ early spring. Some of the interior grasslands (e.g., the Cuyama Valley, Site 3) have as high an amplitude in the second harmonic as in the first. These strong bimodal signals probably indicate the mixture of rain-fed annual grasslands and irrigated agriculture, which maximize productivity at different times. The coastal savanna areas (e.g., Site 2) have a less pronounced second-order amplitude. High elevation areas with closed canopy evergreen cover (e.g., Big Pine Mountain and Pozo Summit) and dry areas with sparse vegetation (e.g., Dry Canyon) exhibit almost no second-order variability in NDVI. The corresponding phase data illustrate the timing of the peak amplitudes (Fig. 9). For the first harmonic, phase values range from 0.5 (beginning of January) to 12.5 (end of December). Through the coastal foothills and valleys the peak NDVI occurs in March to April (e.g., Site 2). The dry interior valleys and ranges peak in late February to early March (e.g., Site 3, Caliente Range, Temblor Range, and Carrizo Plain), corresponding to the period of maximum rainfall in these rapidly emergent annual grassland regions (Fig. 4). A major exception to this pattern is the irrigated agriculture of the San Joaquin Valley (Site 1), which does not express full crop emergence until June/July. The moister, intermediate elevation mountain ranges (e.g., Santa Ynez and Santa Lucia Ranges) peak in May (e.g., Site 6), reflecting the slower response of closed canopy evergreen cover (chaparral) to precipitation. The highest-elevation mountains in the southeast peak last, in mid to late summer (e.g., Site 4 and Mount Pinos), as is expected for these cooler, moister areas that support conifer forests and woodlands. For the second harmonic (Fig. 9b) phase values range from 0.5 (beginning of January) to 6.5 (end of June). An associated peak occurs 6 months later. In general, with a transition from grasslands and woodlands of the valleys and foothills (Site 3) through chaparral and closed oak woodland at intermediate elevations (Site 2) and up to conifer forest at the highest elevations (Site 4), the phase of the second harmonic shifts later into the season. The anomalous phase values surrounding Pozo Summit (Site 6) reflect the influence of a large wildfire (``Highway 58 Fire''). This abrupt event occurred in the summer of 1996 and is not apparent in standard indices derived from the NDVI, such as mean, max, variance, or range. The strongest second-order harmonics are in the interior valleys (Site 3), coastal valleys, and foothill regions (Site 2) and the irrigated agricultural regions (Site 1). The second-order phase values are not meaningful where the second-order amplitudes are close to zero, such as the regions surrounding Dry Canyon, Big Pine Mountain, and Pozo Summit Visualization The distribution of image pixels in mean-amplitudephase space can be visualized in the form of a polar graph

11 A. Moody, D.M. Johnson / Remote Sensing of Environment 75 (2001) 305± Fig. 8. Amplitude data for the first (a) and second (b) DFT harmonics. Units are in NDVI. Compare to the DFT data for the six individual sites as well as to the surface characteristics illustrated in Fig. 1. Fig. 9. Phase data for the first (a) and second (b) DFT harmonics. Units are in months. Compare to the DFT data for the six individual sites as well as to the surface characteristics illustrated in Fig. 1. The distinct feature surrounding point 6 corresponds to a large wildfire in the La Panza range in the summer of This surface anomaly shows up strongly in the second-order phase and also is apparent in the second-order amplitude (Fig. 8).

12 316 A. Moody, D.M. Johnson / Remote Sensing of Environment 75 (2001) 305±323 (Fig. 10). In this representation, the distance from each point to the center of the graph represents the amplitude. The phase is given by a point's azimuthal position. The colors represent each pixel's approximate mean NDVI value. Overall, the growth phase extends from early March to late June (Fig. 10). The main distribution of points appears as an inward clockwise spiral starting in March and moving to August. The group of pixels with high amplitudes that peak in July and August represent irrigated agricultural areas with full emergence in Summer. Buttonwillow (Site 1) is typical of these sites, with moderate mean NDVI values, high amplitudes, and a late phase. The group of pixels with low mean values (blue and indigo) that peak in January/February represent ocean water. Except for these two groups of pixels, amplitudes tend to diminish as the phase shifts later into the growing season. Ranges of mean NDVI values are partitioned into relatively discrete regions. Locations with lower mean NDVI values (green) peak early in the season and exhibit moderate amplitudes. New Cuyama (Site 3) is located near the center of this grouping, which typifies dry interior grasslands that respond quickly to winter and spring rainfall. Areas with intermediate mean NDVI values (yellow) have a larger amplitude and peak primarily from April to May. For example Salsipuedes (Site 2), which supports a mix of chaparral, woodland, productive grasslands, and some agriculture, has a higher mean NDVI and double the amplitude of New Cuyama but is similar in phase. The grass understory responds quickly to winter rain, producing a high amplitude and an early phase similar to New Cuyama, but these areas are more productive due to more abundant precipitation. The evergreen woody vegetation in these areas sustains the fairly high NDVI throughout the year. As the phase shifts to late May and June, the mean NDVI values increase and the amplitudes decrease. These pixels correspond to mid- to upper-elevation locations with chaparral and woodland vegetation, such as Pozo Summit (Site 6), which respond more slowly to seasonal rainfall. The dominance of evergreen vegetation produces the high mean Fig. 10. Polar diagram illustrating the scatter of image pixels in mean-amplitude-phase space for the first DFT harmonic. The colors indicate magnitude of the mean NDVI. Distance from the center represents amplitude. Azimuthal position indicates timing of peak NDVI. Compare to the DFT data for the six individual sites as well as to the surface characteristics illustrated in Figs. 1, 8, and 9.

13 A. Moody, D.M. Johnson / Remote Sensing of Environment 75 (2001) 305± NDVI (red) and the persistence of some grass understory maintains the moderate amplitude. The highest mean NDVI values (red and magenta) have low amplitudes and peak late in the season, from June to July. This is indicative of mid- to high-elevation sites (e.g., Big Pine Mountain) with high biomass, closed canopy evergreen life-forms. Evergreen broadleaf forest, conifer forest, and closed canopy chaparral fit into this category. Dry Canyon (Site 5) typifies the group of pixels with low mean values (cyan) and very low amplitude. These are sparse, dry grassland areas and open semidesert scrub associated with the dry interior valleys and foothills. The polar diagram for the second-order harmonic has six sectors, each of which represents a biannual signal (Fig. 11). Bimodalities are strongest for areas with low to moderate mean NDVI values (yellow and green). The highest second-order magnitudes are associated with irrigated agricultural areas represented by Buttonwillow (Site 1). These points also have the earliest second-order phase. The intermediate second-order magnitudes that peak in March and April are associated with dry interior annual grasslands (New Cuyama Site 3) and woodlands with annual grass understories (Salsipuedes Site 2). Dense evergreen vegetation (red, Sites 4 and 6) and very sparsely vegetated areas (Site 5) have low amplitudes in the secondorder harmonic Image classification The distribution of pixels in mean-phase-amplitude space provides a means for grouping pixels into dominant vegetation formations. We partitioned the data using ISO- DATA clustering (Richards & Jia, 1999) based on the mean NDVI and the amplitude and phase from the first two DFT harmonics. Clusters were merged and class attributes were assigned based on the set of 148 polygons that were sampled in the field throughout the study area in The resulting six classes are not mutually exclusive, but represent a gradient of vegetation status from closed canopy evergreen forest to dry, sparse grasslands (Table 2, Fig. 12). Fig. 11. Polar diagram illustrating the scatter of image pixels in mean amplitude phase space for the second DFT harmonic. Interpretation is the same as Fig. 10. Compare to the DFT data for the six individual sites as well as to the surface characteristics illustrated in Figs. 1, 8, and 9.

14 318 A. Moody, D.M. Johnson / Remote Sensing of Environment 75 (2001) 305±323 Table 2 Amplitude and Phase Values for the First Two Harmonics of the Discrete Fourier Transform for the Six Classes Defined by Unsupervised Clustering of the DFT Outputs Class Color Mean Amp. I Phase I Amp. II Phase II Class Description 1 Yellow :7 Valleys, foothills, and interior uplands: productive grassland, open savanna, some agriculture 2 Red :5 Interior, low elevation, and foothills: sparse grasslands, barren, semidesert scrub, oil fields, urban areas 3 Cyan :3 Valleys: irrigated annual crops, agriculture 4 Blue :0 Foothills and lower-elevation mountains: savanna/open shrub woody savanna/ closed shrub 5 Purple :5 Foothills and lower-elevation mountains: woody savanna with productive grassland and agriculture in small valleys, some lower-elevation evergreen broadleaf forest 6 Green :1 Mid to upper-elevation: closed canopy evergreen broadleaf, or needleleaf forest, some evergreen agriculture A general description of the physiographic setting and vegetation formations are provided for each class. Units for the mean and amplitude values are in NDVI. Units for the phase values indicate months. Phase II values indicate each of the 2 months in which the second harmonic peaks. The color assignments correspond to those used to map the classes in Fig. 12. Yellow = Grassland; Red = Sparse/Barren; Cyan = Irrigated Agriculture; Purple = Savanna/Mixed Savanna 1; Blue = Savanna/Mixed Savanna 2; Green = Evergreen. Class 1 (Grassland; yellow) has a moderate amplitude, an early peak, and an intermediate mean NDVI. These are productive grasslands and open savannas that dominate a northwest ± southeast trending band between the San Joaquin Valley and the major mountain belt in the study area, as well as much of the Santa Maria Valley. Much of this land is used as rangeland. Some agriculture and semidesert scrub areas also fall under this class. Fig. 12. Class map produced using unsupervised clustering based on the mean NDVI and phase and amplitude data from the first and second DFT harmonics. Cluster merging and class labeling (Table 2) are based on 148 field-sampled polygons distributed throughout the study area. Yellow, Grassland; red, Sparse/ Barren; cyan, Irrigated Agriculture; purple, Savanna/Mixed Savanna 1; blue, Savanna/Mixed Savanna 2; green, Evergreen Closed Canopy.

15 A. Moody, D.M. Johnson / Remote Sensing of Environment 75 (2001) 305± Table 3 Comparison of UNC Map with EDC Map Class Total Marg. % 1 2, , , , , , ,668 1,041 3, ,477 6, Total 5,559 1,243 3,372 3,941 7,426 21,541 Marg. % Classes 1 through 6 correspond to the class definitions provided in Table 2. Class 5 has been combined with class 4. Rows represent UNC map classes. Columns represent EDC map classes. 1 = Grassland; 2 = Sparse/ Barren; 3 = Irrigated Annual Crops; 4 = Savanna/Mixed Savanna 1; 6 = Evergreen Closed Canopy. Trace = 11,403 (52.9%). Class 2 (Sparse/Barren; red) occupies a northwest± southeast trending belt just to the southwest of the San Joaquin Valley and is characterized by a low amplitude, an early peak, and a low mean NDVI. This class consists of sparse grasslands, barren areas, semidesert scrub, urban areas, and large oil fields. Class 3 (Agriculture; cyan) represents irrigated agriculture that dominates the San Joaquin Valley and is also present in most valley areas. This class has a large amplitude, a moderate to late peak, and a moderate mean NDVI. Class 4 (Savanna, mixed; blue) represents a range of evergreen cover from savanna/open shrub to woody savanna/closed shrub. This class has a low amplitude, a moderate to late peak, and a high mean NDVI. It is especially abundant at the transition between mid- to upper-elevation closed canopy, evergreen broadleaf vegetation, and lower elevation grasslands, shrublands, and agriculture of the more coastally influenced valleys. Class 5 (Savanna, mixed; purple) has a high amplitude, an early peak, and high mean NDVI. This class, which occurs primarily near the coast between Point Arguello and Point Conception in the Santa Maria Valley and near San Luis Obispo, represents woody savanna with a productive grass understory and also includes lower elevation evergreen broadleaf forest, evergreen agriculture, and small irrigated agricultural fields. Table 4 Comparison of UNC Map with BU Map Class Total Marg. % 1 3, , , , , , , ,097 3, ,236 4,032 6, Total 6,615 1,208 4,150 3,083 6,485 21,541 Marg. % Classes 1 through 6 correspond to the class definitions provided in Table 2. Class 5 has been combined with class 4. Rows represent UNC map classes. Columns represent BU map classes. 1 = Grassland; 2 = Sparse/ Barren; 3 = Irrigated Annual Crops; 4 = Savanna/Mixed Savanna 1; 6 = Evergreen Closed-Canopy. Trace = 10,011 (46.5%). Table 5 Comparison of UNC Map with Field Data Class Total Marg. % Total ,425 Marg. % Classes 1 through 6 correspond to the class definitions provided in Table 2. Class 5 has been combined with class 4. Rows represent mapped classes. Columns represent field polygons. Marginal percentages on the right are producer's accuracies for each class. Marginal percentages on the bottom are user's accuracies for each class. 1 = Grassland; 2 = Sparse/ Barren; 3 = Irrigated Annual Crops; 4 = Savanna/Mixed Savanna 1; 6 = Evergreen Closed Canopy. Trace = 1,647 (67.9%). Class 6 (Evergreen; green) represents closed canopy evergreen forest and shrublands and evergreen orchards. This class dominates the large mountainous belt extending from northwest to southeast through the center of the study area. It is particularly dominant in the higher-elevation mountain complex that occupies the southeast quadrant of the site. This class is characterized by low amplitudes, a late peak, and high mean NDVI values Class map evaluation Map comparisons The class map described above (UNC Map, Fig. 12) is evaluated first by comparison with the EDC and BU land cover products. For all class map evaluations, Classes 4 and 5 were merged because they are both mixed classes that are highly interspersed. The combined class appears as Class 4 in Tables 3, 4, 5, 6, and 7. Overall agreement between our class map and the EDC product is 53% (Table 3). The most common errors occurred between classes that are similar in terms of phenologic characteristics and standing biomass, or that Table 6 Comparison of EDC Map with Field Data Class Total Marg. % Total ,425 Marg. % Classes 1 through 6 correspond to the class definitions provided in Table 2. Class 5 has been combined with class 4. Rows represent EDC mapped classes. Columns represent field polygons. Marginal percentages on the right are producer's accuracies for each class. Marginal percentages on the bottom are user's accuracies for each class. 1 = Grassland; 2 = Sparse/ Barren; 3 = Irrigated Annual Crops; 4 = Savanna/Mixed Savanna 1; 6 = Evergreen Closed Canopy. Trace = 1,659 (68.4%).

16 320 A. Moody, D.M. Johnson / Remote Sensing of Environment 75 (2001) 305±323 Table 7 Comparison of BU Map with Field Data (Test Data) Class Total Marg. % Total ,425 Marg. % Classes 1 through 6 correspond to the class definitions provided in Table 2. Class 5 has been combined with class 4. Rows represent BU mapped classes. Columns represent field polygons. Marginal percentages on the right are producer's accuracies for each class. Marginal percentages on the bottom are user's accuracies for each class. 1 = Grassland; 2 = Sparse/ Barren; 3 = Irrigated Annual Crops; 4 = Savanna/Mixed Savanna 1; 6 = Evergreen Closed-Canopy. Trace = 1,451 (59.8%). represent adjacent points along a continuum of canopy closure (Table 3). For example, 26% of the pixels that were labeled as Savanna in the EDC product were classified as Grassland in the Fourier map. Confusions were also common between other similar class pairs including Sparse/Barren and Grassland (18%), and Evergreen and Savanna (14%). Similarly, 19% of the pixels that were classified as Grassland in the Fourier map were labeled as Savanna on the EDC map. Likewise, Sparse/Barren was confused with Grassland (30%), Agriculture was confused with Grassland (30%), and Savanna was confused with Evergreen (33%). Overall agreement between our class map and the BU product is 46%. Again, the most common confusions were between similar classes (Table 4). Thirty-five percent of the pixels that were labeled as Grassland in the BU product were classified as either Sparse/Barren or Agriculture in the Fourier map. Confusions also occurred between Savanna and Evergreen (40%), Sparse/Barren and Grassland (24%), and Evergreen and Savanna (17%). Similarly, 24% of the pixels that were classified as Sparse/Barren based on the Fourier approach were labeled as Grassland on the BU map. Agriculture was confused with Grassland (35%), and Savanna was confused with both Evergreen (35%) and Grassland (21%). Thirty-three percent of the pixels in the study area were classified the same in all three maps (Fig. 13). Much of the disagreement between maps occurs at the transitions between large homogeneous areas of individual cover types (Fig. 13). In addition, there is considerable confusion in the southwest quadrant of the study area where there is a heterogeneous mixture of Savanna, Evergreen, Agriculture, Grassland, and Sparse/Barren (urban). Much of this area was classified as Savanna (Classes 4 and 5) in the Fourier map. Comparison of the Fourier-based class map and these other products is difficult for several reasons. First, each Fig. 13. Agreement between all three class maps (Fourier-based, EDC, and BU). Yellow, Grassland; red, Sparse/Barren; cyan, Irrigated Agriculture; blue, Savanna/Mixed Savanna; green, Evergreen Closed Canopy.

17 A. Moody, D.M. Johnson / Remote Sensing of Environment 75 (2001) 305± Fig. 14. Distribution of large test regions used to evaluate the Fourier-based classification. Yellow, Grassland; red, Sparse/Barren; cyan, Irrigated Agriculture; blue, Savanna/Mixed Savanna; green, Evergreen Closed Canopy. of the three maps contain error, so disagreements between any two of them can be attributed to error in either map or both maps. For example, the BU map has been determined to have an overall accuracy of 60% (Friedl et al., 2000). Thus, even if the Fourier-based map was 100% correct, agreement between the two maps would not exceed 60%. Second, some disagreements may correspond to misregistration between the three products. Third, the three products were originally produced for different purposes, with different taxonomies, and at different scales. In particular, crosswalking the classification schemes is problematic, and some disagreements between maps may result from the way that classes were relabled. The overall agreement between the EDC and BU maps is roughly 50% Field-based validation The overall accuracy of the Fourier-based map as determined through comparison with the 28 test polygons (Fig. 14) is 68% (Table 5). Producer's accuracy is highest for Agriculture (81%), Savanna (79%), and Evergreen (71%). User's accuracy is highest for Grassland (77%). The most common confusions were between Grassland and Savanna (23%), Sparse/Barren and Agriculture (35%), and Evergreen and Agriculture (25%). In the first case, Savanna with sparse to moderate tree cover can be influenced by the signal of the annual grass understory and thus can easily be confused with Grassland. In the second case, large irrigated agricultural areas include numerous fallow fields that lie almost barren when not irrigated (purple fields in Fig. 1). This leads to confusion between Sparse/Barren and Agriculture. In the third case, many agricultural fields in this area support evergreen orchard crops such as avocado, lemon, or pistachio orchards. These crops are easily confused with the Evergreen class type. The overall correspondence between the field data and the EDC map was also 68%, with notable superiority in the classification of Agriculture (Table 6). The overall correspondence between the field data and the BU map was 60%, with especially poor performance for Savanna (Table 7). 6. Conclusion We find that the phenologies of different land cover types are well articulated in the temporal frequency domain. The mean or 0th-order harmonic indicates the overall level of productivity, providing a basis for discrimination along a gradient from sparse grassland/semidesert scrub to closed canopy evergreen forest. The amplitude characterizes the variability in productivity over the year and differentiates evergreen from deciduous or annual habit. The phase suggests the timing of the green-up in relation to precipitation.