Machine learning for data driven discovery of time transfer functions in numerical modelling: simulating catastrophic shifts in vegetation-soil systems

Abstract

Time transfer functions describe the change of state variables over time in geoscientific numerical simulation models. The identification of these functions is an essential but challenging step in model building. While traditional methods rely on qualitative understanding or first order principles, the availability of large spatio-temporal data sets from direct measurements or extremely detailed physical-based system modelling has enabled the use of machine learning methods to discover the time transfer function directly from data. In this study we explore the feasibility of this data driven approach for numerical simulation of the co-evolution of soil, hydrology, vegetation, and grazing on landscape scale, at geological timescales. From empirical observation and hyper resolution (1 m, 1 week) modelling (Karssenberg et al, 2017) it has been shown that a hillslope system shows complex behaviour with two stable states, respectively high biomass on deep soils (healthy state) and low biomass on thin soils (degraded or desertic state). A catastrophic shift from healthy to degraded state occurs under changes of external forcing (climate, grazing pressure), with a transient between states that is rapid or slow depending on system characteristics. To identify and use the time transfer functions of this system at hillslope scale we follow four procedural steps. First, an extremely large data set of hillslope average soil and vegetation state is generated by a mechanistic hyper resolution (1 m, 1 week) system model, forcing it with different variations in grazing pressure over time. Secondly, a machine learning model predicting the rate of change in soil and vegetation as function of soil, vegetation, and grazing pressure, is trained on this data set. In the third step, we explore the ability of this trained machine learning model to predict the rate of system change (soil and vegetation) on untrained data. Finally, in the fourth step, we use the trained machine learning model as time transfer function in a forward numerical simulation of a hillslope to determine whether it is capable of representing the known complex behaviour of the system. Our findings are that the approach is in principle feasible. We compared the use of a deep neural network and a random forest. Both can achieve great fitting precision, although the latter performs much faster and requires less training data. Even though the machine learning based time transfer function shows differences in the rates of change in system state from those calculated using expert knowledge in Karssenberg et al. (2017), forward simulation appeared to be possible with system behaviour generally in line with that observed in the data from the hyper resolution model. Our findings indicate that discovery of time transfer functions from data is possible. Next steps need to involve the use observational data (e.g., from remote sensing) to test the approach using data from real-world systems. Karssenberg, D., Bierkens, M.F.P., Rietkerk, M., Catastrophic Shifts in Semiarid Vegetation-Soil Systems May Unfold Rapidly or Slowly. The American Naturalist 2017. Vol. 190, pp. E145–E155.