environmentaltools.spatiotemporal.indicators.mean_exceedance_over_total_area

environmentaltools.spatiotemporal.indicators.mean_exceedance_over_total_area(data, thresholds=None)

Compute mean value of exceedances normalized by total area.

Calculates the sum of values exceeding each threshold, normalized by the total number of spatial points. This indicator (MEW - Mean Exceedance over Whole domain) provides a measure of exceedance intensity averaged over the entire spatial domain.

Parameters:

• data (array_like) – 1D array of spatial data values to analyze.

• thresholds (array_like, optional) – Array of threshold values to evaluate. If None, generates 100 equally spaced thresholds from 0 to the maximum data value.

Returns:

• thresholds (np.ndarray) – Array of threshold values used in the analysis.

• mean_exceedances (np.ndarray) – Mean exceedance values normalized by total area.

Notes

The mean exceedance over total area is computed as:

\[MEW(t) = \frac{1}{N} \sum_{i=1}^{N} x_i \cdot \mathbb{1}(x_i \geq t)\]

This indicator represents the spatial average of values that exceed the threshold, with non-exceedance points contributing zero.

Examples

>>> import numpy as np
>>> data = np.random.exponential(5, 1000)
>>> thresholds, mean_exc = mean_exceedance_over_total_area(data)