The Earth Trends Modeler (ETM) is an integrated suite of tools within TerrSet for the analysis of image time series data associated with Earth Observation remotely sensed imagery. With Earth Trends Modeler, users can rapidly assess long term climate trends, measure seasonal trends in phenology, and decompose image time series to seek recurrent patterns in space and time.

**With ETM, users can address such questions as:**

- “How have temperatures changed over the past 30 years?”
- “Are plants exhibiting a later senescence?”
- “Are there recurrent spatial patterns in phytoplankton productivity?”
- “What are the geographic impacts of climate events such as El Niño?”

No other software technology provides such a coordinated suite of data mining tools needed by the earth system science community for climate change analysis and impact assessment.

**Tools in ETM include:**

- Parametric and non-parametric trend measures
- Seasonal trend analysis
- Principal Components / Empirical Orthogonal Function analysis (PCA/EOF)
- Extended PCA/EOF for the co-analysis of multiple series (EPCA/EEOF)
- Multichannel Singular Spectrum Analysis (MSSA)
- Empirical Orthogonal Teleconnection (EOT) analysis and extended modes
- Canonical Correlation Analysis (CCA)
- Lagged Linear Modeling
- Fourier PCA and Wavelet analysis

While ETM is intended for professional use, its simple and intuitive interface makes it an excellent tool for teaching and self-exploration. The system includes a full tutorial and sample data sets.

**Earth Trends Modeler Key Features**

- Extract and analyze long-term global trends and their impacts
- Examine the relationship between time series
- Examine trends in seasonality
- Isolate true change from normal environmental variability
- Uncover and analyze patterns of variability across temporal scales
- Preprocess image time series data including noise removal and deseasoning

## Earth Trends Modeler Analytical Features

- Animated 3-D display of space-time cubes
- Dynamic lag correlation between index time series
- Interactive Maximum Overlap Discrete Wavelet analysis
- Trend analysis of index time series (linear trend, Theil-Sen median trend, polynomial (up to 9th order), moving average, Gaussian moving average, moving maximum)
- Interactive temporal profiling
- Image series trend analysis (linear trend, degree of linearity, Theil-Sen median trend, monotonic trend, Mann-Kendall trend significance)
- Seasonal Trend Analysis (STA) including interactive interpretation and trend significance mapping
- Principal Components (PCA) / Empirical Orthogonal Function (EOF) analysis (T-mode and S-mode, standardized/unstandardized and centered/uncentered)
- Extended PCA/EOF (T-mode and S-mode, standardized/unstandardized and centered/uncentered)
- Multichannel Singular Spectrum Analysis (T-mode and S-mode, standardized/unstandardized and centered/uncentered)
- Empirical Orthogonal Teleconnection (EOT) analysis (S-mode, standardized/unstandardized and centered/uncentered)
- Extended EOT (S-mode, standardized/unstandardized and centered/uncentered)
- Cross-EOT (S-mode, standardized/unstandardized and centered/uncentered)
- Multichannel EOT (MEOT) (S-mode, standardized/unstandardized and centered/uncentered)
- Canonical Correlation Analysis (CCA) (T-mode and S-mode, standardized/unstandardized and centered/uncentered)
- Fourier PCA (S-mode, unstandardized, centered)
- Index to Image Series and Image to Image Series Multiple Linear Modeling (slope, intercept, R, R2, Adjusted R2, Partial R) at multiple lags plus residual series creation
- Missing Data Interpolation (harmonic interpolation, spatial interpolation, linear temporal interpolation and climatology)
- Denoising via temporal filtering (mean, Gaussian mean, maximum, cumulative sum, cumulative mean) with any arbitrary filter length
- Denoising via Maximum Value Compositing (MVC).
- Denoising via PCA (T-mode and S-mode)
- Denoising via Inverse Fourier Analysis
- Deseasoning (anomalies, standardized anomalies, temporal filter)
- Series generation (linear, SIN, COS)
- Series editing (lagging, truncation, extension, skip selection, temporal aggregation, spatial subsetting, automatic renaming)
- Serial correlation analysis (Durbin-Watson)
- Detrending (linear or difference series)
- Cochrane-Orcutt transformation
- Trend-preserving prewhitening (Wang and Swail procedure)