Taylor’s law in satellite time series of vegetation productivity

Background: Taylor’s law is considered a semi-natural-law and originally comes from ecology. It describes how the variance of a quantity grows with its mean, following variance = a · mean^b. It was first found for insect and animal counts, but it also shows up in many other data. The exponent b tells us something about stability. If b is below 2, places with high values fluctuate less, relative to their mean, than places with low values. With Landsat data back to 1985, this can be tested for vegetation at every pixel.

Short description: The thesis tests Taylor’s law with long satellite time series of vegetation, for example from Landsat. For each pixel, a robust yearly vegetation measure is derived, and its mean and variance over the years are calculated. The relationship between mean and variance across all pixels then gives the exponent b. Comparing b between land cover types, regions or elevation zones shows where vegetation is more or less stable. Part of the work is to check how far the results depend on the choice of vegetation index and on the number of available observations.

Taylor’s law from satellite time series (schematic). Each Landsat pixel becomes one point, and the slope b shows how variability scales with productivity.

Suggested reading

Taylor, L. R. (1961). Aggregation, variance and the mean. Nature, 189, 732–735. https://www.nature.com/articles/189732a0

Badgley, G., Field, C. B., & Berry, J. A. (2017). Canopy near-infrared reflectance and terrestrial photosynthesis. Science Advances.

Vadrevu, K. (2026): Power law scaling reveals systemic divergence in fire risk across South and Southeast Asian countries. Environmental Research Letters. 10.1088/1748-9326/ae962a

Start: Anytime

Prerequisites/qualification

·        Remote Sensing & GIS

·        Basic programming skills

·        Good basic statistics (regression, power laws)

·        Interest in ecology