The Earth Trends Modeler (ETM) is specially designed for the analysis of image time series from earth observing systems such as the instruments on NASA’s Terra and Aqua satellites or the NASA/JAXA TRMM (Tropical Rainfall Measuring Mission) satellite. It includes a coordinated suite of data mining tools for the extraction of trends and underlying determinants of variability, and will be of special importance to scientists focused on climate change and ecosystem dynamics.

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.

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.

Analyze variability across varying temporal scales. For example, 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.

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.

Analyze long-term trends with 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.

Examine trends in seasonality, such as phenological change in plant species, with a newly developed procedure for Seasonal Trend Analysis. 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.

Utilize Principal Components Analysis (also known as Empirical Orthogonal Function Analysis) for the decomposition of a series into its underlying constituents (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.

Uncover characteristic patterns of variability over space-time with 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.

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.

Examine relationships between series using 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).

Preprocess and edit series with a suite of utilities 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.