Time series analysis
From Wiki
Contents |
Spatial time series analysis and presentation
I have been working with a 20 year time series of monthly global satellite data including the Global Inventory Modeling and Mapping Studies (GIMMS) normalized difference vegetation index (NDVI) dataset, and other global data including Reynolds Optimal Interpolation sea surface temperature (SST) based on satellite and surface data, at one degree spatial resolution, to examine climate systems and seasonal change on the earth as periodic processes, on time scales ranging from two months to twenty years, as an introduction to climate study and modeling.
- Global Inventory Modeling and Mapping Studies (GIMMS): http://glcf.umiacs.umd.edu/data/gimms
- Reynolds Optimum Interpolation of Sea Surface Temperature (v.2): http://podaac.jpl.nasa.gov/reynolds
NDVI response to variation in precipitation and hydrologic flux in semiarid regions
The response of vegetation and land cover to weather and climate that is observed in remote sensing is complicated by many factors, especially local details of topography, soil, land cover type, species mix and other ecosystems factors, as well as basic climate parameters. It is extremely difficult to provide a generalized model of vegetation's role in atmospheric processes, although it is known to be large, because of many interacting biophysical mechanisms. The problems in modeling vegetation are also in a sense the converse of the problems in modeling the lower troposphere: rather than high temporal variability of a well-mixed fluid with limited spatial variability over relatively large areas, vegetation and other landcover shows high (and often fixed) spatial variation and slow temporal variation. (Dickinson, "Land surface", in Climate System Modeling, ed. Trenberth 1992) Temporal variation in NDVI is dominated by the annual phenology cycle of greenup, growth, and senesence, in various forms, but with great local variability, and characterizing that variability is an important open problem in modeling the role of the terrestrial biosphere in climate change. (Sellers, "Land surface process modeling", op.cit.)
Temporal variation of NDVI sometimes is not slow; in particular, greenup of semiarid land is extremely sensitive to weather events as well as climate. Remote sensing time series of NDVI could offer the potential of observation of spatial variation in greenup onset and rate, in semiarid regions, to detect ecotones that can provide sensitive indicators of climte change -- with sufficient temporal resolution in NDVI datasets. In most NDVI data collected from satellite imagery, cloud cover is one of the main technical problems, and compositing of observations over a time period -- selection of the maximum value observed for each pixel in a period, as representative of that period -- is the usual method of obtaining land cover observations during periods of cloud cover. Polar satellites such as the NOAA AVHRR series which obtain at most one image of a location per day, typically provide biweekly composite observations of NDVI. These biweekly series must be again composited to monthly series for use in tropical regions. The result is a lack of readily available NDVI data with sufficient temporal resolution to provide useful data for measuring greenup delay.
In arid and semiarid areas, however, cloud cover may not be as significant a problem. Using the GIMMS NDVI data set at biweekly temporal resolution, with corresponding temperature and precipitation data, I hope to measure greenup time in several semiarid regions, and provide maps of local and temporal variation in greenup delay, which might yield useful ecotome information in conjunction with land cover and land use data.
Horn of Africa
In the Horn of Africa, complex terrain and climate circumstances produce a great variety of land cover and ecosystems. In 2005, with fellow Clark student Mathewos Tamiru, whose work on famine early warning and relief introduced me to the profound impacts of climate change in this region, I attempted a merged precipitation dataset using surface and satellite observations. The result had insufficient coverage in arid regions, poor interpolation results in other regions, and was not a realistic starting point. In the past year improved merged precipitation data has become available through the NASA Global Precipitation Climatology Project (GPCP) in monthly estimates for an archive beginning in 1979. Although this is also insufficent temporal resolution, it is a beginning that may make it possible to establish methods for study of event-based NDVI response to weather as well as climate trends.
Average JJAS-Meher season rainfall in Ethiopia (M.Tamiru)
18Y Average NDVI (Brown)
Temporal principal components analysis (Eastman and Fulk, 1993) applied to an NDVI time series for this region showed a monsoon-like variation in semiarid NDVI as well as the annual cycle in plateau NDVI in this region:
Components 1 (dominant) and 2 (annual) of 18Y montlhy NDVI series TSA
Components 3 (monsoon-like) and 4 (semiannual) of 18Y montlhy NDVI series TSA
Component 3 loadings, 18y
Somali Current
This monsoon-like component may be related to seasonal changes in offshore winds and currents in the Indian Ocean, esp. the Somali Current, a western boundary current with strong cold upwelling and seasonal reversals.
Central Asia climate time series
The second such semiarid region I've studied is Central and Southwest Asia, where modeling of vegetation response to anomalous precipitation, snowmelt, runoff, and stream flow conditions might help explain the origin, progress, and outcome of a recent extreme drought.
From 1998 to 2001, severe drought persisted across a large area of Central and Southwest Asia, including Iran, Afghanistan, Pakistan, Turkmenistan, Uzbekistan, and Tajikistan, affecting 60 million people in a grave humanitarian crisis aggravated by chronic political instability in many parts of this region, and war in Afghanistan. A 2001 study by the International Research Institute or Climate and Society (IRI) at Columbia University examined the severity of the drought in Central and Southwest Asia and its possible causes. This period showed record temperatures worldwide and a number of global climate anomalies generally associated with a strong "La Nina" phase of the ENSO process; but the region suffered a long-term precipitation deficit as well as high temperatures, creating a drought more severe than any in the region in the previous fifty years.
Vegetation, especially agriculture, in this region depends on snowmelt from mountainous regions as well as precipitation, and in one interpretation of data on this drought, a disruption of normal snowmelt patterns by climate change, with early snowmelt in late winter rather than spring, and possible depletion of mountaintop snowpack, might contribute to the drought's destruction of vegetation in various ways. A detailed examination of vegetation response to temperature, precipitation, snowmelt, runoff, and stream flow might show such mechanisms in progress.
Data for most of these parameters is available. With UML-EEAS climatologist Prof Mathew Barlow, a co-author of this report, I am examining time series of temperature, precipitation, stream flow, and vegetation for a selected set of flow gauge locations in the headwaters of the Amu Darya and Sir Darya river systems in Uzbekistan and Tajikistan. Monthly stream flow data archives have been maintained (although sometimes erratically) for over a century, the most complete data being in the last half of the century, with some discontinuity at the end of the Soviet period. Vegetation index data is of course available at 0.1 degree spatial resolution from the GIMMS archive, with biweekly time resolution, for 1981-2003. The period of overlap of this archive, with readily available stream gauge data, is 1981-1985; data exists for some gauges through the present, but is less readily available. Precipitation archives based on merged satellite and surface observations are now available from NASA. Watershed area estimates are available for many gauge locations, and for others can be calculated from GIS elevation data. Runoff from watersheds due to known precipitation can also be calculated using GIS tools.
It may therefore be possible to estimate snowmelt runoff as the excess of stream flow over expected runoff due to precipitation, first for the period 1981-1985, and second for the period surrounding the 1998-2002 drought. With these two sources of flow separated, it may be possible to identify and model vegetation response to these separate hydrologic processes: while precipitation affects a broad area, snowmelt flow might be expected to affect riparian regions in possibly narrow valleys. Using GIS tools to identify buffer regions on stream centerlines, it may be possible to measure these effects in vegetation, to help understand their importance during the drought. Modeling of these effects may have benefits in forecasting vegetation response to hydrology and climate change.
Work on this topic is progressing using web access to share graphic and interactive mapserver visualization of this data and intermediate products: see the Central Asia Climatology viewer with USGS base maps at the UML-EEAS ArcIMS Mapserver. For more information contact Alex Brown or Mathew Barlow.
Time and frequency domain decomposition of NDVI and SST time series
In 2006 I began a study of time series analysis and modeling of remote sensing image data time series (HTML) (PDF) with Ron Eastman of Clark University, which became my MA thesis. I worked with a 20 year time series of monthly global normalized difference vegetation index (NDVI), sea surface temperature (SST), and their combination, at one degree spatial resolution, to examine climate systems and seasonal change on the earth as periodic processes, on time scales ranging from two months to twenty years, as an introduction to climate study and modeling. While the twenty year series is both too short to show many definitive climate change indicators, and too coarse in time to show brief or high-frequency events including many anthropogenic changes, it does show some indicators of climate change, and provides an excellent view of the physical processes of global circulation on a broad spatial scale.
This study was concerned with identification of processes in climate time series, by separation of data time series of into trend, seasonal, and irregular time scale component series, and interpretation of these components. Separation processing used a combination of time and frequency domain filtering methods based on Clark University's Idrisi GIS software (Eastman 1987-2006). A trend time series simplifies examination of long-period and interannual phenomena by removing annual and seasonal variation, the strongest component of variation by far, and smoothing irregular high-frequency components, random event noise, and observation error. A seasonal time series extracts data variation at the time scale of the annual cycle and its harmonics, showing the weather and climate variation that is most evident to us in day-to-day observation. An irregular high-frequency component is the residual variation at time scales shorter than the principal harmonics of the annual cycle, which can illustrate presence of brief periodic phenomena, short random events, and observation noise and error, in their spatial distribution.
This study covered a broad range of processing, analysis, and presentation methods, with an emphasis on partitioning of variance in both the temporal and the spatial domain.
Partitioning of variance using principal components analysis in the time domain (Eastman and Fulk 1993) provided maps of characteristic variation modes for trend, seasonal, and irregular series, with univariate loadings time series showing temporal correlation of these modes. By use of the univariate discrete Fourier transform, these loadings time series yielded characteristic spectra of these modes in the frequency domain. These maps, loadings series and their spectra made it possible to identify climate process features such as ENSO and NAO in the trend series, and semiannual and complex temporal variation as well as the annual cycle, in seasonal and irregular climate series. Correlations with well-known univariate climate time series also produced maps of distribution of possible climate change effects.
Partitioning of variance in the power spectrum of the source series produced by temporal Fourier transform, into the frequency bands of the derived trend, seasonal, and irregular series, produced summary maps for each time scale showing contribution to total variation on each time scale:
NDVI+SST annual/seasonal series contribution to total variance
NDVI+SST interannual/trend series contribution to total variance
NDVI+SST irregular series contribution to total variance, showing outlier "hot spots" (see below)
This partitioning of variance in the power spectrum provides estimates of relative strength of climate processes as well as their time scale. The annual cycle, of course, dominates variation on the earth's surface. Peak NDVI+SST variation on an annual scale was almost an order of magnitude greater than either peak trend varation or peak irregular variation. Variation in SST was dominated by the annual cycle in midlatitudes, with trend contributions by ENSO, an interannual climate process over the eastern tropical Pacific where little seasonal or irregular variation was observed. Peak trend variation in NDVI was roughly double that of irregular variation. Spatial location of high variation in NDVI assisted in identification of climate processes, esp. annual boreal forest snowcover. Locally high trend variation of NDVI in Amazonia might be identified with climate change, or anthropogenic land cover conversion; but locally high irregular variation of NDVI in this region might also be identified with artifacts in data collection such as persistent cloud cover and temporal compositing of satellite observations, long used to circumvent it. (Animation shows moving patterns of NDVI change over Amazonia that suggest atmospheric rather than land cover processes.) Other outlier points of high irregular variation in NDVI observed at coastal locations might be due to artifacts in data processing, esp. registration of NDVI and SST, but might also be of anthropogenic origin.
Known and possibly observed sources of error in these observations include:
- Masking of periodic phenomena, esp. interannuals, by inconsistency of spatial distribution
- Intermittent cloud cover obscuring NDVI observation
- NDVI compositing error due to jitter in time sampling
- A possible northern-southern hemisphere difference in observation or processing, producing high variance artifacts at a small number of coastal locations in the southern hemisphere
- Excess contribution of high latitudes to some computations due to latlong projection – esp. TSA component loadings, which are a full-raster correlation of the component image with each time sample image (optionally masked)
- Possible remaining error due to variation in AVHRR instruments over time, after GIMMS team corrections in NDVI and Reynolds team corrections in SST
- Quantization noise due to encoding of full scale (across time series, not frame-by-frame) in [0..255] byte values
- Frequency domain processing artifacts
- Computational error accumulation
Directions for future work include:
1. Repeat on full resolution data. This requires a substantially greater computational resources and software toolset. By examining 0.1 degree NDVI (3600x1800 pixels) data and similar resolution SST it may be possible to observe fine structure of spatial distribution of temporal features, and clarify the nature of outliers. With a full high-resolution decomposition available, “windowed” series of study areas are easy to extract and examine much more economically.
2. Repeat with atmospheric and precipitation data. Circulation of air and water, the working fluids of the global heat engine, and the causal link between solar heating and its response in SST and NDVI, has been invisible here. Adding a global precipitation time series, e.g. NASA Global Precipitation Climatology Project (GPCP), may provide a view of this causal link, esp. through phase relationships in the frequency domain, which may make it possible to observe delays between solar heating, precipitation, and vegetation response. In particular, it may be possible to measure greenup delays corresponding to known land cover type classifications, from the temporal Fourier transform phase product.
For more information see this page. A summary discussion with links is available here and conclusions here.
New data sources
Merged satellite-surface precipitation data archive
High temporal resolution NDVI from geostationary satellite
- "Comparisons of Compositing Period Length for Vegetation Index Data from Polar-orbiting and Geostationary Satellites for the Cloud-prone Region of West Africa". Rasmus Fensholt, Assaf Anyamba, Simon Stisen, Inge Sandholt, Ed Pak, and Jennifer Small. PE&RS v73n3 March 2007 pp.297ff
- Abstract: "Land surface data from MODIS and AVHRR have been extensively used for vegetation monitoring. In cloud-prone areas like West Africa the use of Normalized Difference Vegetation Index (NDVI) data for vegetation monitoring is hampered by persistent cloud cover especially during the rainy season. The new geostationary satellite Meteosat Second Generation (SEVIRI MSG) is the first geostationary satellite suited for vegetation monitoring allowing NDVI to be derived with a 15-minute temporal resolution. For West Africa, MODIS (combined TERRA and AQUA) produce above 85 percent cloud-free pixels in the scene during the entire rainy season using 16-day composite periods. SEVIRI MSG data produces>98 percent cloud-free pixels during the entire season using a 3-day composite period. Therefore, there is a much higher probability for producing high quality cloud free data using SEVIRI MSG data for a short time composite period compared to Polar Orbiting Environmental Satellite (POES) data, which is expected to substantially improve various applications of satellite based natural resource management, including vegetation monitoring, in West Africa."
METOP: European polar satellite replaces NPOESS?
See METOP.
