Tracking states and transitions in semiarid rangelands: A spatiotemporal archetypal analysis of productivity dynamics using wavelets

Abstract

Climate change poses challenges in classifying ecosystem dynamics, as they are influenced by shifting dynamics resulting from changes in climate forces and meteorological variables, including temperature and water availability. To address this, our study presents a novel approach using Continuous Wavelet Transform (CWT) and power spectrum analysis to classify vegetation dynamics, considering the time-dependent variability of ecosystem frequencies. We applied our method to centred and standardized MODIS NDVI time series for the period 2000–2021, using an experimental field station in northern Patagonia as a case study. By performing a continuous wavelet transform on the data for each pixel, we obtained instantaneous power spectra, capturing variability across different dates and pixels. These spectrums were then consolidated into a comprehensive database, and subsequently classified using archetypal analysis. We identified a convex combination of archetypal spectrums that best represented the entire power spectrum database. Mapping the resulting archetypes and their weights in both space and time allowed us to explore pixels' variations in archetype weights in relation to factors such as time, topography, and climate. In addition, to examine the potential relationship between the NDVI time series and climate drivers, we computed the Average Cross-Wavelet Power Spectrum (ACWPS) to different climatic indices. Three archetypes were sufficient to explain the majority of power spectrum variability in the study area. These archetypes exhibited distinctive characteristics: 1) medium-frequency variability (2–4 years), 2) low-frequency variability (>4 years), and 3) an annual (i.e. seasonal) cycle with low-frequency variability. Spatially, the first two archetypes were predominantly observed in highland steppes, while the third archetype prevailed in lowland areas associated with meadows. At the beginning of the studied period, Archetypes 1 and 3 dominated, but after the Puyehue-Cordón Caulle Volcanic Complex eruption in 2011 their prominence diminished, and Archetype 2 became more prevalent in the whole study area. Finally, all three NDVI series representative of archetypes showed a relative peak at approximately four years, which could be linked to the Indian Ocean Dipole variability. These results highlight an abrupt shift in the system's behaviour, primarily related to changes in variability distribution rather than mean values. This disturbance-induced transition aligns with the theory of state and transitions in ecological system dynamics. We propose that the states in this model are not fixed but represent alternative dynamic behaviours, akin to different types of limit cycles. Consequently, employing a wavelet analysis-based classification method provides a robust means of studying and understanding such variability and transitions, thereby offering clarity and comprehension of ecosystem states. Notably, this methodology proves particularly effective for large databases of detailed time series.