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Contents 1 NDVI 1.1 Phenology and greenup 1.1.1 Phenology 1.1.1.1 Schwartz and Karl (1990) 1.1.2 Defining and detecting greenup 1.1.2.1 TIMESAT (Per Jönsson and Lars Eklundh, 2002) 1.1.2.1.1 Jönsson and Eklundh: Seasonality Extraction by Function Fitting to Time-Series of Satellite Sensor Data (2002) (PDF) 1.1.2.1.2 Jönsson and Eklundh: TIMESAT — a program for analyzing time-series of satellite sensor data. (2004) (PDF) 1.1.2.1.3 TIMESAT exploration of CSWA Aral Sea Basin 1982-2002 1.1.2.1.3.1 Change in greenup 1982-1986 vs 1997-2002 1.1.2.2 Zhang et al (2003) 1.1.2.3 IDRISI Taiga (Eastman 2009) 1.1.2.3.1 STA exploration of CSWA Aral Sea Basin 1982-2002

NDVI

Time series of vegetation related global-scale imagery can be used for study of phenology, the timing and variation of seasonal ecological and climate processes. Modern approaches are based on tracking the temporal change of a vegetation index such as Normalized Difference Vegetation Index (NDVI) to make use of vegetation's typically low reflection in the red, and strong reflection in the near infrared (NIR). Infrared light energy is reflected by plants due to their cellular structure, and red light is mostly absorbed by growing plants for photosynthesis. The normalized difference vegetation index is constructed in such a way that the attenuated reflected sunlight energy (1% to 30% of incident sunlight) is amplified by ratio-ing red and NIR:

Due to its robustness and simplicity, NDVI has become one of the most popular remote sensing based products, and phenological interpretation of NDVI time series is widespread, despite its limitations.

Phenology and greenup

Phenology

Phenological studies of a wide variety of phenomena have been recorded since the eighteenth century. Traditional phenological methods recorded the annual first occurrences of individual species and phenophases, correlating dates with temperature and other surface observations. The annual onset of greenup, in which many plants break dormancy and begin foliage production, takes place as seasonal change such as day length increase approaches its maximum rate; and the definition of greenup has been associated with observation of a variety of different specific biological changes. The great variety of species and events, however, makes it difficult to choose a biological definition of greenup. Literature on this topic includes:

1. Mark Schwartz, Karl, T.R, "Spring Phenology: Nature's Experiment to Detect the Effect of "Green-Up" on Surface Maximum Temperatures" Monthly Weather Review, 1990 118:883-890. PDF HTML
2. Per Jönsson and Lars Eklundh, TIMESAT (2002)
3. Xiaoyang Zhang, Mark A. Friedl, Crystal B. Schaaf, Alan H. Strahler, John C.F. Hodges, Feng Gao, Bradley C. Reed, Alfredo Huete. "Monitoring vegetation phenology using MODIS." Remote Sensing of Environment 84 (2003) 471–475 PDF HTML
4. Jeremy Fisher; Richardson, A.D.; Mustard, J.F. "Phenology model from surface meteorology does not capture satellite-based greenup estimations" Global Change Biology (2007) 13, 707–721, doi: 10.1111/j.1365-2486.2006.01311. PDF HTML

Schwartz and Karl (1990)

Such classical phenology definitions can however be used in quantitative modeling of climate events. Meteorologists Schwartz and Karl (1990), using data from a northeastern US study on the lilac Syringa chinensis, used the day number of the appearance of the first leaf as an event defining the origin on a time scale of temperature and other meteorological observations, to see if it would be possible to improve forecasting using the date of this event as a predictor variable. A "hypsometric" model temperature based on the thickness (700 hPa height - 850 hPa height) of the boundary layer, and phenological variables based on day number of first leaf, were used in a regression model predicting the daily maximum temperature. Their results showed that this event took place with the maximum rate of increase of daily temperature, and that the onset of transpiration of moisture after first leaf immediately reduced this rate by as much as 3.5 deg C biweekly (less in areas near major water bodies). This first leaf event was also linked to transition in the change in average observed surface atmospheric water vapor pressure.

Defining and detecting greenup

TIMESAT (Per Jönsson and Lars Eklundh, 2002)

Detecting a "first leaf" event in NDVI time series from satellite observations is nearly impossible due to noise in data, mostly but not exclusively negatively biased due to cloud cover and other problems in observation. While noise can be reduced by smoothing in time or averaging groups of years, this obscures significant variation in time. Fitting an estimated vegetation vigor index to the upper envelope of the NDVI time series can be done by various methods. Jonsson and Eklundh (2002) developed methodology and algorithms, and provide software tools that implement them. Using the fitted index curve, a variety of rules for measuring phenological timing can be applied. Like many others, they use a threshold in index change to detect spring greenup: first occurrence of an increase over the base level, of 10% of the range to the index maximum over the year.

• Per Jönsson and Lars Eklundh: Seasonality Extraction by Function Fitting to Time-Series of Satellite Sensor Data. IEEE Transactions On Geoscience And Remote Sensing, Vol. 40, No. 8, August 2002 (PDF)
• --, Seasonality extraction from satellite sensor data. (2003) In Frontiers of Remote Sensing Information Processing, edited by Chen. C.H . World Scientific Publishing. pp 487-500. (PDF)
• --, TIMESAT — a program for analyzing time-series of satellite sensor data. Computers & Geosciences 30 (2004) 833–845. (PDF)
• --, TIMESAT 2.3 User's Manual (2007) (PDF)

Jönsson and Eklundh: Seasonality Extraction by Function Fitting to Time-Series of Satellite Sensor Data (2002) (PDF)

"A new method for extracting seasonality information from time-series of satellite sensor data is presented. The method is based on nonlinear least squares fits of asymmetric Gaussian model functions to the time-series. The smooth model functions are then used for defining key seasonality parameters, such as the number of growing seasons, the beginning and end of the seasons, and the rates of growth and decline. The method is implemented in a computer program TIMESAT and tested on Advanced Very High Resolution Radiometer (AVHRR) normalized difference vegetation index (NDVI) data over Africa. Ancillary cloud data [clouds from AVHRR (CLAVR)] are used as estimates of the uncertainty levels of the data values. Being general in nature, the proposed method can be applied also to new types of satellite-derived timeseries data."

Jönsson and Eklundh (2002) Fig. 2. Fitted functions around a maximum from the two-step procedure. The dashed line shows the fitted function from the first step, and the solid line the fit from the second step. The original NDVI time-series is shown by the noisy fine continuous line.

Fig. 7. Start of the first growing season of 1991, estimated from the fitted functions. Time is in decades going from 1 (January 1–10) to 36 (December 21–31). The small graph shows the variation in date over the marked transect across the Sahel.

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Jönsson and Eklundh: TIMESAT — a program for analyzing time-series of satellite sensor data. (2004) (PDF)

"Three different least-squares methods for processing time-series of satellite sensor data are presented. The first method uses local polynomial functions and can be classified as an adaptive Savitzky–Golay filter. The other two methods are more clear cut least-squares methods, where data are fit to a basis of harmonic functions and asymmetric Gaussian functions, respectively. The methods incorporate qualitative information on cloud contamination from ancillary datasets. The resulting smooth curves are used for extracting seasonal parameters related to the growing seasons. The methods are implemented in a computer program, TIMESAT, and applied to NASA/NOAA Pathfinder AVHRR Land Normalized Difference Vegetation Index data over Africa, giving spatially coherent images of seasonal parameters such as beginnings and ends of growing seasons, seasonally integrated NDVI and seasonal amplitudes. Based on general principles, the TIMESAT program can be used also for other types of satellite-derived time-series data."

TIMESAT exploration of CSWA Aral Sea Basin 1982-2002

Alex Brown 00:48, 22 April 2009 (EDT)

TIMESAT implements a general seasonality analysis of either image or univariate (or single-pixel) time series, using several heuristics. First, the series is fit approximately to the first two harmonics of the given annual period (i.e. annual and seminannual sinusoids) to count the number of seasons. (This is much like the HANTS process in IDRISI Taiga ETM.) In the tropics, where more than one season per year is common, this determines whether the location does in fact show more than one; elsewhere the step is necessary to initialize the remaining heuristics.

This is followed by application of any of three local-fit upper envelope filters, each of which uses a well-defined curve family to generate spline fits to the raw sensor data, with heuristic rules for discarding samples showing negatively biased noise. (Negative biased noise is typical of cloud artifacts; cloud mask metadata can also be used with weighting.) Parameters control the behavior of this spline fitting to one or more of:

• asymmetrical Gaussian curves
• asymmetrical logistic curves
• Savitsky-Golay (SG) local filter using polynomial curves, with adaptively varying window size.

The intent of spline fitting is to provide an upper envelope to NDVI data that follows recorded NDVI closely rather than replacing it with an interpolation from a curve family with inherent periodic structure, esp. sinusoids. Gaussian and logistic splines tend to smooth rapidly changing data without temporal distortion, but often do not preserve rapid change. SG filtering uses variable order of polynomial and variable window size to support smoothing that tends to preserve rapid change, by using large residuals to trigger reduction of window size. This produces a filtered time series that can follow rapidly changing NDVI quite closely.

The authors provide a sample NDVI dataset for the west African Sahel, where all these features show their value. The Sahel, like most arid and semiarid landscapes, shows areas of very rapid greenup in response to precipitation, and NDVI shows sudden change, not a smooth annual cycle.

Using TIMESAT components (written in Fortran-90, provided as executables) it was possible to prepare an exploration of phenology in the Aral Sea Basin for the period 1982-2001. This subset of the 1981-2003 GIMMS NDVI dataset was determined by the way TIMESAT was used: TIMESAT appears to require a minimum of three annual periods in an image timeseries, hence the 1982-2003 period was divided into overlapping three-year groups of 72 biweekly samples each -- 1982-1984, 1983-1985, ... 2001-2003. (1981 data was incomplete.) Savitsky-Golay filtering was used with recommended parameters. Eleven phenology variable images are generated, as described above; in this exploration only "start of season" is provided here, defined as date (i.e. sample number) on which NDVI for a pixel has risen by 20% of its amplitude for the year. This produced twenty maps of this index:

• http://gis.uml.edu/abrown2/ca/phenology/timesat/1s1/index.html

The study period drought is shown very clearly in the change in start-of-season from 1997 through 2001, where it is evident that large areas vegetated in 1998 never showed greenup in 1999 and 2000:

• 

.

Change in greenup 1982-1986 vs 1997-2002

Start-of-season was averaged over the first five and last five years of the series, and the resulting index of change in greenup is mapped:

• 

This map of "Change in season start" in the study area is the difference between the mean greenup date in the first and last five year segments of the archive series, in "biweek" (1/24th year) time units. Most of the desert area shows slight advance of greenup by one or two weeks (yellow-green); mountainous areas show advance of 4 weeks or more on north slopes and desertification (no greenup) on south slopes. The agricultural valleys north of the Pamirs (Fergana Valley) and other areas in the Amu Darya and Syr Darya valleys seem to show months of advance of greenup, possibly indicating vegetation through the winter. Modification to TIMESAT to work with a single year, and integration of elevation and independent land cover - land use data, is necessary to try to better understand these features; but it's clear there's a pronounced change in phenology over the period.

(That map may be a bit difficult to interpret; this map which overlays precipitation reanalysis, elevation, and watershed delineation with study areas and national borders may help. The NDVI study area is the maroon overlay in the center of the figure, around the watershed boundaries (cyan); the Aral Sea is in its northwest quadrant, Afghanistan along its south side, and the Pamirs on the east side.)

Zhang et al (2003)

Zhang et al (2003) adopt a similar envelope fitting method using piecewise logistic functions, in phenological analysis of MODIS BRDF-corrected NDVI (NBAR), but identify the date of spring greenup onset with the maximum curvature of the fitted logistic function, at the beginning of the spring season.

1. Previous: Xiaoyang Zhang; Hodges, J.C.F.; Schaaf, C.B.; Friedl, M.A.; Strahler, A.H.; Feng Gao, "Global vegetation phenology from AVHRR and MODIS data," IGARSS'01 - IEEE International Geoscience and Remote Sensing Symposium, 2001. Proceedings pp.2262-2264 vol.5, 2001 URL PDF - see discussion

Zhang et al (2001) Fig. 1. Phenological transition points and phases.

"Accurate measurements of regional to global scale vegetation dynamics (phenology) are required to improve models and understanding of inter-annual variability in terrestrial ecosystem carbon exchange and climate–biosphere interactions. Since the mid-1980s, satellite data have been used to study these processes. In this paper, a new methodology to monitor global vegetation phenology from time series of satellite data is presented. The method uses series of piecewise logistic functions, which are fit to remotely sensed vegetation index (VI) data, to represent intra-annual vegetation dynamics. Using this approach, transition dates for vegetation activity within annual time series of VI data can be determined from satellite data. The method allows vegetation dynamics to be monitored at large scales in a fashion that it is ecologically meaningful and does not require pre-smoothing of data or the use of user-defined thresholds. Preliminary results based on an annual time series of Moderate Resolution Imaging Spectroradiometer (MODIS) data for the northeastern United States demonstrate that the method is able to monitor vegetation phenology with good success."

"... The annual cycle of vegetation phenology inferred from remote sensing is characterized by four key transition dates, which define the key phenological phases of vegetation dynamics at annual time scales. These transition dates are:

1. greenup, the date of onset of photosynthetic activity;
2. maturity, the date at which plant green leaf area is maximum;
3. senescence, the date at which photosynthetic activity and green leaf area begin to rapidly decrease;
4. dormancy, the date at which physiological activity becomes near zero.

Because of the spatial, temporal, and ecological complexity of these processes, simple methods to monitor them from remote sensing have proven elusive. Here, we present a new method, which fits satellite VI data to a logistic function of time. Based on this function, the four transition dates defined above can be identified."

Zhang et al (2003) Fig. 1. An idealized trajectory of vegetation index values with multiple growth periods described using several logistic models.

Zhang et al (2003) Fig. 2. A schematic showing how transition dates are calculated using minimum and maximum values in the rate of change in curvature. The solid line is an idealized time series of vegetation index data, and the dashed line is the rate of change in curvature from the VI data. The circles indicate transition dates. The extreme values located between each circle indicate the point at which the rate of change in curvature changes sign.

Zhang et al (2003) Fig. 3. A sample time series of MODIS EVI data and estimated phenological transition dates for a mixed forest pixel in New England. The dashed line with diamonds is the original EVI data and the solid line with stars is the fitted logistic models.

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IDRISI Taiga (Eastman 2009)

Alex 00:47, 22 April 2009 (EDT)

The raster GIS product named after the renowned mediaeval Arab geographer Muhammed al-Idrisi (Eastman 1987-, http://www.clarklabs.org) provides a number of application workbench components that address aspects of land use and land use change modeling, often including new research methods. The most recent is IDRISI Taiga Earth Trends Modeler (ETM, 2009) which provides an integrated workbench for exploration and analysis of remote sensing time series. While smoothing and fitting of NDVI and other series data is supported, ETM implements a "STA (Seasonal Trend Analysis)" method, "closely based on the procedure known as HANTS (Harmonic Analysis of Time Series) by Roerink, et al., (2000)" that differs significantly from earlier work, by adopting harmonic analysis.

"Seasonal trend analysis (STA) is a new analytical technique developed by Clark Labs. It uses two stages of time series analysis to map out trends in the shape of the seasonal curve. It can be used with any series that exhibits seasonality. In the first stage, each year of data is submitted to a harmonic regression to yield the following shape parameters:

• An annual mean image (sometimes called Amplitude 0).
• An image expressing the amplitude of the annual cycle (a sine wave with one cycle over the year), known as Amplitude 1.
• An image expressing the phase angle of the annual cycle (an indication of where on a sine curve the beginning of the series is located). This is known as Phase 1.
• An image expressing the amplitude of a semi-annual cycle (a sine wave with two cycles over the year), known as Amplitude 2.
• An image expressing the phase angle of a semi-annual cycle (an indication of where on a sine curve the beginning of the series is located). This is known as Phase 2.

"These five parameters can describe an exceptionally large family of curves. By using only two harmonics and the mean, high frequency noise and variability are rejected.

"The first stage results in five images per year – one for each of the five shape parameters. Then in the second stage of the analysis, a Theil-Sen median trend is run on each of the shape parameters over the total number of years in the series. Since the median trend has a breakdown bound of 29% of the length of the series, interannual trends shorter than this length are also rejected. Thus the result of the two stages yields a focus on long-term trends in the seasonal curve while rejecting both high frequency noise and low frequency variability."

The purpose is visualization of a generalized amplitude and phase offset presentation plot of the seasonality of a remote sensing variable at any pixel or sample region. One option in this plot is identification of greenup and greendown points, at a threshold level of the full range of the variable over the generalized plot. Mapping of this date as a derived raster variable does not seem to be provided.

• Eastman et al., (in press) “Seasonal Trend Analysis of Image Time Series,” International Journal of Remote Sensing.
• Roerink, G.J., Menenti, M., and Verhoef, W., (2000) “Reconstructing cloudfree NDVI composites using Fourier analysis of time series”, International Journal of Remote Sensing, 21, 9, 1911-1917. (Abstract, references and comments)

STA exploration of CSWA Aral Sea Basin 1982-2002

Alex Brown 28 March 2009

• (MS Word)
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• In some locations observed NDVI shows advancement of greenup by approximately one month from first to final period, and significant reduction later in the year.
• Other locations show little change in seasonality of NDVI. Generally these are forested locations closer to eastern headwaters of basins.
• STA harmonic regression significantly distorts representation of seasonality of NDVI, even with three harmonics. Even when the general form of the seasonal cycle is correct, there is significant displacement in time.
• STA estimates of greenup based on threshold of maximum (by default 40%) are performed using the fitted seasonal curves and are therefore not reliable. (Available on “Explore STA” panel.)