Data analysis techniques for the coastal zone
Here we introduce a series of Coastal Wiki articles dealing with data analysis techniques. Data analysis techniques are used to identify patterns and relationships in observational data, to reduce data complexity, to interpolate missing information and to predict variables from available observations. Some techniques also help to identify possible relationships between observed variability and external forcing factors.
The data analysis techniques presented in the Coastal Wiki are:
- Linear regression
- Principal component analysis, empirical orthogonal functions and singular spectrum analysis
- Wavelets
- Artificial neural networks
- Kriging
- Random Forest Regression
- Support Vector Regression
These techniques serve different purposes: regression and machine learning are primarily used to describe relationships and make predictions, principal component analysis and wavelets to identify patterns of variability, and kriging to interpolate spatially distributed observations.
The reliability of predictions should always be assessed using independent validation data. For coastal datasets, observations are often correlated in space and time; validation procedures should account for these correlations to avoid overestimating predictive accuracy. The ability of a method to reproduce the available observations does not necessarily imply that it can reliably predict future conditions.
Each technique has advantages and disadvantages. The most suitable technique depends on the problem at hand and on the quantity and quality of the available data. In the table below we provide some guidance for choosing the most appropriate technique for the analysis of data on coastal processes.
| Analysis technique | Strengths | Limitations | Application example |
|---|---|---|---|
| Linear regression analysis | * Estimation of trends and relationships between variables * Simple implementation and interpretation |
* Requires an appropriate choice of regression function * Sensitive to outliers * Correlated residuals complicate uncertainty estimation * Extrapolation is unreliable if the fitted relationship does not remain valid |
Estimation of shoreline retreat rates or trends in water quality from repeated surveys |
| Principal component analysis, empirical orthogonal functions and singular spectrum analysis | * Purely data driven * Can handle large data sets * Identification of dominant patterns of variability * Enables data reduction and noise removal |
* Results depend on data centering, scaling and weighting * Individual modes do not necessarily correspond to distinct physical processes * Propagating or phase-shifted patterns may require combinations of several modes |
Identification of dominant spatial or temporal patterns in bathymetric and shoreline observations or ecological monitoring data |
| Wavelets | * Analysis of non-stationary signals and transient or localized features * Can handle large data sets * Enables data reduction and noise removal * Reveals patterns that hint towards possible underlying processes |
* Standard implementations generally require regularly spaced data * Short records limit scale resolution and increase boundary effects * Less efficient than Fourier or harmonic analysis for stationary periodic signals |
Identification of transient events and changing periodicities in water-level, temperature or chlorophyll records |
| Artificial Neural Networks | * Learning from training data * Can provide uncertainty estimates * Can handle complex nonlinear systems * Ranking of predictor relevance (not causal) |
* Often requires substantial training data, depending on network complexity * Predictions outside the range of training conditions are generally unreliable * Black box prediction tool * No general prescription for optimal network design * Possibly unreliable results due to overfitting * No guarantee for convergence to optimal solution |
Prediction of shoreline position, water quality or algal blooms from environmental forcing variables |
| Kriging | * Best linear unbiased interpolation under an appropriate spatial covariance model * Provides uncertainty estimate * Can handle non-uniform sampling |
* Correlations of data deviations from the interpolated function vanish at large distance * Requires sufficient observations to estimate spatial correlation reliably * Sensitive to variogram specification (bias by outliers and skewness) |
Spatial interpolation of bathymetry, sediment contamination or benthic species abundance from scattered observations |
| Support Vector Regression | * Curve fitting based on machine learning from training data * Handles nonlinear relationships * Works well with small to medium-sized datasets * Less sensitive to outliers than least squares fitting * The optimization has no inferior local minima * Predictions depend only on the support vectors |
* The kernel function and its settings, together with the tolerance and penalty settings, must be chosen * Computing time increases rapidly with the size of the dataset * No uncertainty range for predictions; known measurement errors can only be used as weights * Does not directly show the importance of predictor variables * Poor at extrapolation beyond the range of the training data |
Prediction of wave height, turbidity or chlorophyll concentration from a limited number of observations |
| Random Forest Regression | * Prediction tool based on machine learning from training data * Handles nonlinear relationships * Relatively robust to noise and outliers * Can efficiently handle large datasets and many predictor variables * Less prone to overfitting than a single tree * Provides measures of the predictive importance of predictor variables |
* Less readily interpretable than a single regression tree * Variable-importance measures can be misleading when predictors are strongly correlated * Poor at extrapolation beyond conditions represented in the training data |
Prediction of habitat suitability, species abundance or water quality from multiple environmental predictors |
Related articles
- Linear regression analysis of coastal data
- Analysis of coastal processes with Empirical Orthogonal Functions
- Wavelet analysis of coastal processes
- Artificial Neural Networks and coastal applications
- Data interpolation with Kriging
- Random Forest Regression
- Support Vector Regression
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