Earth scientists utilize image time series data to model and analyze earth trends and dynamics. Time series data is especially useful for global climate change research and analysis. The Earth Trends Modeler (ETM) is a GIS software solution especially designed for the analysis of image time series data. It includes a coordinated suite of data mining tools for the extraction of trends and underlying determinants of variability.
Why Use Earth Trends Modeler and IDRISI?
- IDRISI is the outcome of over 20 years of geospatial technology development.
- IDRISI is engineered by expert scientists and research practitioners.
- Earth Trends Modeler is the only software available for the full exploration of image time series data.
With Earth Trends Modeler, you can:
- View animations of series in a space-time cube format, allowing views of the series over space, time and space-time.
- Explore profiles of a series over time.
- Analyze long-term trends with a variety of techniques for trend analysis, including measures of linearity, monotonicity, and trend rate.
- Examine trends in seasonality, such as phenological change in plant species, with a newly developed procedure for Seasonal Trend Analysis.
- Utilize Principal Components Analysis (also known as Empirical Orthogonal Function Analysis) for the decomposition of a series into its underlying constituents.
- Uncover characteristic patterns of variability over space-time with the Empirical Orthogonal Teleconnection (EOT) method.
- Explore for the presence of cycles in the series utilizing Fourier-PCA.
- Examine relationships between series using a linear modeling (multiple regression) tool.
- Preprocess and edit series.
Analyze variability across varying temporal scales
In the illustration in Figure 1, 25 years of monthly sea surface temperature in the Labrador Sea are analyzed. The colors in the wavelet diagram indicate cooling or warming. The X axis represents time while the Y axis represents scale (in months). On time scales greater than approximately 6 years, we only see warming in this region. However, a major cooling event is seen in 1989 with an impact that lasted for a little over 6 years. Similarly in 1998-2000, we see a cooling period that took 3 years to develop and recover. This procedure utilizes an Inverse-Haar Wavelet analysis. The triangular wavelet analysis diagram shows the nature and scale of variations in sea surface temperature. The animated globe shows variations in ocean height which are closely related with temperature variations.
Figure 1: An analysis of trends in sea surface temperature from 1982 to 2006. The strong monotonic trend of increasing temperature in the Atlantic is seen to be related to the Atlantic Multidecadal Oscillation (AMO) as determined from a temporal regression with four major climate teleconnection indices.
Explore profiles of a series over time
Profiles may be saved as index series which may then be used as input for a regression analysis. For example, in Figure 2, a profile is extracted of monthly anomalies in vegetation condition (NDVI) over the 22 year period from 1982-2003, and then saved as a series. This series is then used as the independent variable in a regression with sea surface temperature. The result indicates that the area of the ocean whose sea surface temperature anomalies most closely co-varies with vegetation anomalies in southeast Massachusetts is the Canary Current off of Africa. Note that the Canary Current and the Gulf Stream are both important components of the North Atlantic subtropical gyre and commonly exhibit a dipole relationship in temperature.
Figure 2: An example of temporal profiling (of NDVI anomalies in southeast Massachusetts) followed by subsequent analysis of its relationship with global sea surface temperatures using the linear modeling tool.
Analyze long-term trends
Earth Trends Modeler includes a variety of techniques for trend analysis, including measures of linearity, monotonicity, and trend rate (see Figure 3). A special trend estimation tool is also included that is robust to the effects of outliers. Known as a Theil-Sen Median Slope estimator, it is unaffected by wild values until they exceed 29% of the length of the series. Associated measures of trend non-parametric significance are also provided.
Figure 3: An illustration of several trend measures. The top image measures linearity in trends in sea surface temperature. As can be seen, the most linear trends include increases in the East and West Greenland currents and the Labrador Sea (all parts of the North Atlantic Subpolar Gyre), and the region at the mouth of the Amazon, most particularly, the Orinoco River.
Examine trends in seasonality
Earth Trends Modeler includes a newly developed procedure for Seasonal Trend Analysis to view trends in seasonality, such as phenological change in plant species. While vegetation phenology is an evident application, the tool can be applied to any data set that exhibits a seasonal response to environmental conditions. Figure 4 presents an illustration of this tool. The procedure combines the logic of Windowed Fourier Analysis with non-parametric trend analysis. The colors represent different types of trends in the seasonal curve of vegetation photosynthesis. The graph shows vegetation photosynthetic activity (Y-axis) for each of the 12 months (X-axis) of 1982 (in green) and 2003 (in red) for the area circled in France. As can be seen, the red color that is found over most of Europe relates to increased photosynthetic activity through the winter and spring. Note that by looking at the graph, one can see that spring is coming about a month earlier in 2003 than it was in 1982.
Figure 4: A Seasonal Trend Analysis of vegetation conditions in Europe for the period 1982-2003 based on an analysis of vegetation index imagery from the AVHRR instrument on the NOAA Polar Orbiter satellites (shown in the space-time visualization cube).
Utilize Principal Components Analysis
Decompose a series into its underlying constituents with Principal Components Analysis (also known as Empirical Orthogonal Function Analysis) (Figure 5). PCA/EOF is probably the most commonly used procedure for the analysis of image time series as used in the geographic and climatological communities. Both standardized and unstandardized PCA are provided.
Figure 5: A Principal Components Analysis of monthly precipitation imagery from 1979-2006 reveals
the impact of the El Nino / La Nina phenomenon. The loading chart at the left shows its evolution over
time. The chart at the top left shows a space-time plot of precipitation anomalies over time (vertical
dimension) and all longitudes (horizontal dimension) at the equator. This is also known as a Hovmoller
plot.
Uncover characteristic patterns of variability over space-time
Earth Trends Modeler includes the Empirical Orthogonal Teleconnection (EOT) method. EOT relaxes the strict orthogonality of Principal Components Analysis (where the components are independent in both space and time) to maintain only the condition of independence in time. The result is essentially the same as that of rotated components but is both simpler to understand and does not require subjective parameter choices. Both EOT analysis (for single series) and Cross-EOT analysis (for two series) are provided. EOT can be used for example to determine areas in the ocean that can best explain variability in other areas of the ocean with regards to surface temperature. The Cross-EOT procedure can be used for example to determine what areas of the ocean show temperature patterns that best explain variations in vegetation conditions on the land.
Figure 6: The area in the oceans (top, yellow through red) determined to have the most significant impact on growing conditions in Southern Africa (bottom, the area in red experiencing the greatest impact). This mapping results from an analytical procedure known as Empirical Orthogonal Teleconnection analysis. Information such as this can be used in the development of Early Warning Systems.
Explore for the presence of cycles in the series
Utilizing Fourier-PCA, the three-step analysis first conducts a Fourier decomposition of the series into a sequence of phase and amplitude images for a family of sine waves. The amplitudes are then analyzed for characteristic patterns of waves using Principal Components Analyses. In the third stage, image correlation analysis relates these characteristic patterns back to time. Figures 7 and 8 show some results from this experimental technique.
Figure 7: An illustration of the output from Fourier-PCA using the frequency plot view. This one is quite simple to understand. The component is associated with locations that show a strong presence of 25 sine wave cycles over the 25 years of the series. It thus represents the degree to which an annual cycle is present.
Figure 8: Another illustration of Fourier-PCA. Component 4 from the same analysis as above showed a very difficult combination of frequencies to interpret. The loadings view (graph) however shows that the pattern is associated with a linear trend. The red areas in the top image thus indicate areas that are warming (a negative negative). Most of the world’s oceans show this effect. The region in the central Pacific though, affected by the extraordinary variability of the ENSO cycle, shows a residual cooling effect (ENSO appeared in Components 2 and 3 of this analysis). The bottom image shows that the pattern in the Atlantic shares some similarity to that of the Atlantic Multidecadal Oscillation, but is substantially different.
Examine relationships between series
Earth Trends Modeler provides a linear modeling (multiple regression) tool. Options are provided for a variety of outputs (R, R2, adjusted R2, slope and intercept images, partial R images and residual series). Relationships can be examined between image series and index series (such as climate teleconnection indices) or between image series and multiple independent image series (see Figure 9).
Figure 9: The partial correlation images for the Pacific DecadalOscillation (top) and the Atlantic Multidecadal Oscillation (bottom) after removing the effects of the ENSO (El Nino / Southern Oscillation) and the North Atlantic Oscillation phenomena. In this analysis, climate indices for these four teleconnections were used as independent variables while monthly anomalies in sea surface temperature were the dependent variable. Each pixel is analyzed independently.
Preprocess and edit series
A suite of utilities are included which allow for the interpolation of missing data (such as from cloud contamination), and the denoising and deseasoning of a series. Tools are also provided for the testing for serial correlation (Durbin-Watson), trend-preserving, prewhitening to remove series correlation in residuals, and significance testing in the presence of serially correlated residuals utilizing the Cochrane-Orcutt transformation.
The Earth Trends Modeler is a special extension within IDRISI Taiga in a manner paralleling the Land Change Modeler (LCM). Developed under a grant from the Gordon and Betty Moore Foundation, Earth Trends Modeler provides an opening salvo on the tools that science requires to monitor our changing planet.
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