Feature Extraction for Spatiotemporal Dependencies

In this section, we will do a deeper dive into how one can further preprocess the data to remove extreme values

• Spatially Aggregate Data (Optional)
• Temporally Aggregate Data (Optional)
• Stitching, SuperImposing, Aggregating, Batch Sampling - PoPPY

Examples

• 1D Data Recorded in a sequence of distance or time
• 2D sampling for spatial interpolation
• 3D sampling for spatial interpolation
• Spatiotemporal

Spatial Scale

• Changes —> Mean, Variance, Tails, Range, Distribution Shape
• Tools —> Variogram, Predict the scale
• Recale:
  • DownScale/SuperResolution/UpSample
  • Upscaling/Coarsen/DownSample —> Average Arithmetic, Power Law Average, Harmonic, Geometric
• Aggregations
• Creating location weights - https://youtu.be/k9VbyqafnPk?si=biWcgcqwuXVe8RfG

# filtering - remove high/low frequency signals
# spatiotemporal peaks - spatial,temporal dependencies
# remove climatology - temporal dependencies
# spatial aggregation - spatial dependencies
# rolling mean - spatial, temporal dependencies

Cookbook

• Spatial Statistics with Declustering Weights —> Grid Cell Size vs Declustered Mean
• Lat-Lon Spatial Averages using weights at poles

Example PsuedoCode¶

First, we need some spatiotemporal data. This data could be any spatiotemporal field, $y=y(\mathbf{s},t)$, representing the extreme values we wish to extract.

y: Array["Dt Dy"] = ...

Now, we need to do some preprocessing steps to ensure that we get an iid dataset. We will remove some of the excess effects.

# filter high frequency signals
y: Array["Dt Dy"] = low_pass_filter(y, params)
# remove climatology
climatology["Dclim"] = calculate_climatology(y, reference_period, params)
y: Array["Dt Dy"] = remove_climatology(y, climatology, params)
# spatial aggregation
y: Array["Dt"] = spatial_aggregator(y, params)

Now, we need to select some extreme values.

y_max: Array["Dt"] = block_maximum(y, params)