Gaussian Process Empirical Dynamic Modeling

Novel data-driven method to model the nonlinear dynamics of leafing phenology

Ecological forecasting
First-author
Awarded
AGU 2020 presentation, ESA 2021 presentation (E.C. Pielow Award)
Authors

Yiluan Song

Stephan B. Munch

Kai Zhu

Published

August 4, 2021

Keywords

global change biology, environmental data science, phenology, climate change, forecasting, GPEDM, machine learning

Highlights

  • We used a novel data-driven method of Gaussian Process Empirical Dynamic Modeling (GPEDM) to forecast forest and grassland vegetative phenology.
  • This nonparametric model accounts for nonlinear relationships with environmental variables and past phenology, outperforming traditional parametric methods.
  • The model allowed us to fill in historical data, forecast future data, infer drivers, estimate green-up dates, and simulate impacts of climate change.
  • This approach has the promise to improve predictions of phenology and understanding of complex environmental responses.

GPEDM

Gaussian Process time-delay embedding model with a spatial covariance function layer Sugihara et al., 2012.

Empirical dynamic modeling through time-delay embedding Munch et al., 2017.

This study

Study area for forest land cover in the NEON domain Appalachians_Cumberland Plateau. Raster mask represents pixels with forest land cover. Orange points represent locations of PhenoCams. Study area for grassland land cover in the NEON domain Pacific Southwest. Raster mask represents pixels with grassland land cover. Orange points represent locations of PhenoCams.

Workflow of this study.

One-step ahead predictions

Observed forest EVI in black and predicted forest EVI in purple.

Observed grassland EVI in black and predicted forest EVI in purple. Accuracy of in-sample predictions and three types of out-of-sample predictions (extrapolation over time, over space, over both time and space)for forest EVI. Accuracy of in-sample predictions and three types of out-of-sample predictions (extrapolation over time, over space, over both time and space)for grassland EVI.

Multi-steps ahead forecasts

Observed forest EVI in black and forecasted forest EVI in blue starting from black verticle line.

Observed forest EVI in black and forecasted grassland EVI in blue starting from black verticle line.

Inference

Inferred length scale () showing the influence of predictors at different lags on response (grassland EVI) at different day of year, with larger values of suggesting more important influence of a predictor on the response.

Inferred functional relationships between the response (forest EVI) and two predictors as examples.

Green-up date

Forest green-up date estimated from observed EVI and EVI from one-step ahead predictions, in in-sample tests and three types of out-of-sample tests (extrapolation over time, over space, over both time and space). Forest green-up dates estimated from observed EVI and EVI from multi-steps ahead forecasts.

Climate change

Forecasted forest EVI under 1°C increase in temperature at one pixel in two years as an example. Forest green-up dates estimated from observed EVI and EVI from multi-steps ahead simulations under 1°C warming.

PhenoCam Greenness

Observed forest PhenoCam greenness in black and forecasted forest PhenoCam greenness in blue starting from black verticle line. Observed grassland PhenoCam greenness in black and forecasted grassland PhenoCam greenness in blue starting from black verticle line.