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

Abstract

The turbulent fluxes of momentum, heat and water vapour link the Earth's surface with the atmosphere. Therefore, the correct modelling of the flux interactions between these two systems with very different timescales is vital for climate and weather forecast 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 differences in the flux calculations; furthermore, the underlying equations are non-linear and have to be solved iteratively at each time step of the model. In this study, we tried a different and more flexible approach, namely using an artificial neural network (ANN) to calculate the scaling quantities u* and θ* (used to parameterise the fluxes), thereby avoiding function fitting and iteration. The network was trained and validated with multi-year data sets 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; moreover, this ANN performed considerably better than a multivariate linear regression model. Similar satisfying results were obtained when the ANN routine was implemented in a one-dimensional stand-alone land surface model (LSM), paving the way for implementation in three-dimensional climate models. In the case of the one-dimensional LSM, no CPU time was saved when using the ANN version, as the small time step of the standard version required only one iteration in most cases. This may be different in models with longer time steps, e.g. global climate models.