Harmonic Analysis of Time-Series AVHRR NDVI Data

Harmonic analysis of a one-year time series (26 periods) of NOAA AVHRR NDVI biweekly composite data was used to characterize seasonal changes for natural and agricultural land uselland cover in Finney County in southwest Kansas. Different crops (corn, soybeans, alfalfa) exhibit distinctive seasonal patterns of NDVI variation that have strong periodic characteristics. Harmonic analysis, also termed spectral analysis or Fourier analysis, decomposes a time-dependent periodic phenomenon into a series of sinusoidal functions, each defined by unique amplitude and phase values. The proportion of variance in the original time-series data set accounted for by each term of the harmonic analysis can also be calculated. Amplitude and phase angle images were produced from analysis of the time-series NDVI data and correlated with information on crop type and extent for the region to develop a methodology for crop-type identification. Crop types occurring in southwest Kansas, including corn, winter wheat, alfalfa, pasture, and native prairie grasslands, were characterized and identified using this technique and biweekly AVHRR composite data for 1992. For crops with a simple phenology, such as corn, the majority of the variance was captured by the first and additive terms of the harmonic analysis, while winter wheat exhibited a bimodal NDvI periodicity with the majority of the variance accounted for by the second harmonic term. Introduction Recent advances in remote sensing technology and theory have expanded opportunities to characterize the seasonal and interannual dynamics of natural and managed vegetation cornmunities. Studies have shown that the temporal domain of multispectral data frequently provides more information about vegetation cover and condition than the spatial, spectral, or radiometric domains (Briggs and Nellis, 1991; Kremer and Running, 1993; Eastman and Fulk, 1993; Samson, 1993; Reed et al., 1994). Time series analysis of Advanced Very High Resolution Radiometer (AVHRR) multispectral imagery has allowed scientists to examine regionalto global-scale phenological phenomena such as greenup, duration of green period, onset of senescence, and changes in seasonally dependent biophysical variables such as leaf area index (LAI), biomass, and net primary productivity (Tucker et al., 1985; Roller and Colwell, 1986; Achard and Brisco, 1990; Eastman and Fulk, 1993; Reed et al., 1994; Lancaster et al., 1996; Myneni et al., 1997). Approaches to the analysis of time series remotely sensed imagery have varied considerably, from standardized principal component analysis (Eastman and Fulk, 1993), to textural M.E. Jakubauskas and J.H. Kastens are with the Kansas Applied Remote Sensing (KARS) Program, University of Kansas, Lawrence, KS 66045 ([email protected]) D.R. Legates is with the Department of Geography, University of Delaware, Newark, DE 19716-2541. analysis (Briggs and Nellis, 1991), to the development of phenological metrics that describe seasonal changes in the normalized difference vegetation index (NDVI) (Lloyd, 1990; Samson, 1993; Reed et al., 1994). While metrics defined by Lloyd and Reed et al. are excellent descriptions of a particular time-series phenomenon and have found general acceptance and application in ecology and agriculture (Loveland et al., 1995; Reed et al., 1996; Kastens et al., 1997; Reed and Yang, 1997; Tieszen et al., 1997;), they do not represent a true time-series analyses, defining instead the characteristics of a time-series phenomenon (e.g., the height, magnitude, duration, or area of the timeseries curve). In this paper, we describe the application of harmonic analysis (also known as Fourier analysis) to a 26-period time series of NOAA-AVHRR NDVI biweekly composite NDVI data of Finney County, Kansas. We discuss the theory behind harmonic analysis (NA) of time series, some applications of oneand two-dimensional harmonic analysis of time-series data in other research fields, and the application of HA specifically to a time-series of satellite imagery. Within the scope of this paper, we discuss only the application of the HA to a single year of NOAA-AVHRR data (26 periods), focusing on five specific landuselland-cover types common to the study area (irrigated corn, winter wheat, irrigated alfalfa, native shortgrass prairie, and native sandsage prairie as case examples of the harmonic analysis applied to time-series imagery. Ovewlew of Harmonic Analysis Briefly defined, harmonic (Fourier) analysis permits a complex curve to be expressed as the sum of a series of cosine waves (terms) and an additive term (Rayner, 1971; Davis, 1986). Each wave is defined by a unique amplitude and a phase angle, where the amplitude value is half the height of a wave, and the phase angle (or simply, phase) defines the offset between the origin and the peak of the wave over the range 0 to 2 r (Figure la). Each term designates the number of complete cycles completed by a wave over the defined interval (e.g., the second term completes two cycles) (Figure lb). Successive harmonic terms are added to produce a complex curve (Figure lc), and each component curve, or term, accounts for a percentage of the total variance in the original time-series data set. Fourier analysis has been used in digital image processing for analysis of a single image as a two-dimensional wave form (Jensen, 1996; Schowengerdt, 1997), and more recently has been used for analyzing sets of successive regular multidate samples of satellite remotely sensed imagery (Andres et al., 1994; Olsson and Eklundh, 1994; Verhoef et al., 1996; Azzali and Menenti, 2000). Photogrammetric Engineering & Remote Sensing Vol. 67, No. 4, April 2001, pp. 461-470. 0099-11 12/01/6704-461$3.00/0