Vegetation responses to variations in climate: A combined ordinary differential equation and sequential Monte Carlo estimation approach

Vegetation responses to variation in climate are a current research priority in the context of accelerated shifts generated by climate change. However, the interactions between environmental and biological factors still represent one of the largest uncertainties in projections of future scenarios, since the relationship between drivers and ecosystem responses has a complex and nonlinear nature. We aimed to develop a model to study the veg-etation's primary productivity dynamic response to temporal variations in climatic conditions as measured by rainfall, temperature and radiation. Thus, we propose a new way to estimate the vegetation response to climate via a non-autonomous version of a classical growth curve, with a time-varying growth rate and carrying capacity parameters according to climate variables. With a Sequential Monte Carlo Estimation to account for complexities in the climate-vegetation relationship to minimize the number of parameters. The model was applied to six key sites identified in a previous study, consisting of different arid and semiarid rangelands from North Patagonia, Argentina. For each site, we selected the time series of MODIS NDVI, and climate data from ERA5 Copernicus hourly reanalysis from 2000 to 2021. After calculating the time series of the a posteriori distribution of pa-rameters, we analyzed the explained capacity of the model in terms of the linear coefficient of determination and the parameters distribution variation. Results showed that most rangelands recorded changes in their sensitivity over time to climatic factors, but vegetation responses were heterogeneous and influenced by different drivers. Differences in this climate-vegetation relationship were recorded among different cases: (1) a marginal and decreasing sensitivity to temperature and radiation, respectively, but a high sensitivity to water availability; (2) high and increasing sensitivity to temperature and water availability, respectively; and (3) a case with an abrupt shift in vegetation dynamics driven by a progressively decreasing sensitivity to water availability, without any changes in the sensitivity either to temperature or radiation. Finally, we also found that the time scale, in which the ecosystem integrated the rainfall phenomenon in terms of the width of the window function used to convolve the rainfall series into a water availability variable, was also variable in time. This approach allows us to estimate the connection degree between ecosystem productivity and climatic variables. The capacity of the model to identify changes over time in the vegetation-climate relationship might inform decision-makers about ecological transitions and the differential impact of climatic drivers on ecosystems.