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

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.

Estimation of the Surface Fluxes for Heat and Momentum in Unstable Conditions with Machine Learning and Similarity Approaches for the LAFE Data Set

“…Furthermore, the momentum flux should be studied. Leufen and Schädler (2019) used an extensive set of tower data and compared these with retrievals of MOST and an MLP. They investigated the surface momentum and sensible heat fluxes, simultaneously.…”

“…After training the MLP using the data of one tower and application of the training results to an independent data set of another tower, Leufen and Schädler (2019) found comparable performance of MOST and MLP. Latent heat fluxes were not investigated.…”

“…They demonstrated promising training results; however, Safa et al (2018) neither investigated temperature nor moisture gradients in the SL nor compared the results with MOST or BRN. Leufen and Schädler (2019) used an extensive set of tower data in combination with MOST and an MLP to study surface momentum and sensible heat fluxes.…”

Spatial and Temporal Analysis of Land Surface Temperature Change on New Britain Island

“…The estimation used in the model is the multivariate normal maximum likelihood and ordinary least squares (OLS). The equation of multivariate regression (Leufen & Schädler, 2019) is:…”

Can machine learning improve the model representation of TKE dissipation rate in the boundary layer for complex terrain?

“…Machine-learning techniques can successfully capture the complex and nonlinear relationship between multiple variables without the need of representing the physical process that governs this relationship. They have been successfully used to advance the understanding of several atmospheric processes, such as convection (Gentine et al, 2018), turbulent fluxes (Leufen and Schädler, 2018), and precipitation nowcasting (Xingjian et al, 2015). The renewable energy sector has also experienced various applications of machine-learning techniques, in both solar (Sharma et al, 2011;Cervone et al, 2017) and wind (Giebel et al, 2011;Optis and Perr-Sauer, 2019) power forecasting.…”