Calculating the turbulent fluxes in the atmospheric surface layer with neural networks

Lukas Hubert Leufen, Gerd Schädler

Geoscientific model development · 24 May 2019 · Karlsruhe Institute of Technology (KIT), Forschungszentrum Jülich / Jülich Supercomputing Centre

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In one sentence. A one-hidden-layer neural network replaces Monin–Obukhov stability functions for surface-layer fluxes, matching the standard method at seven flux sites.

Abstract

Abstract. The turbulent fluxes of momentum, heat and water vapour link the Earth's surface with the atmosphere. The correct modelling of the flux interactions between these two systems with very different time scales is therefore vital for climate (resp. Earth system) models. Conventionally, these fluxes are modelled using Monin–Obukhov similarity theory (MOST) with stability functions derived from a small number of field experiments; this results in a range of formulations of these functions and thus also in the flux calculations; furthermore, the underlying equations are non-linear and have to be solved iteratively at each time step of the model. For these reasons, we tried here a different approach, namely using an artificial neural network (ANN) to calculate the fluxes resp. the scaling quantities u* and θ*, thus avoiding explicit formulas for the stability functions. The network was trained and validated with multi-year datasets from seven grassland, forest and wetland sites worldwide using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) quasi-Newton backpropagation algorithm and six-fold cross validation. Extensive sensitivity tests showed that an ANN with six input variables and one hidden layer gave results comparable to (and in some cases even slightly better than) the standard method. Similar satisfying results were obtained when the ANN routine was implemented in a one-dimensional stand alone land surface model (LSM), opening the way to implementation in three-dimensional climate models. In case of the one-dimensional LSM, no CPU time was saved when using the ANN version, since the small time step of the standard version required only one iteration in most cases. This could be different in models with longer time steps, e.g. global climate models.

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