Abstract
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.
Highlights
The turbulent fluxes of momentum, heat, water vapour and trace gases link the atmosphere with the Earth’s surface.the faithful representation of these fluxes is essential for climate and weather forecast models to function properly
If the mean squared error (MSE) on the validation set rises continuously, training is stopped to prevent overfitting. Following this training and validation stage, the ability of the selected artificial neural network (ANN) to generalise is tested on data that are completely new to the ANNs
The validation results from ANNs with six inputs and one single hidden layer trained under six-fold cross-validation with random data splitting are shown in the box-andwhiskers plot in Fig. 3 as a function of the number of hidden neurons
Summary
The faithful representation of these fluxes is essential for climate and weather forecast models to function properly. In these models, the fluxes are parameterised as momentum flux τ = ρu2 ∗ and heat flux H −ρ cp u∗ θ∗. In the framework of the almost exclusively used Monin–Obukhov similarity theory (MOST; Monin and Obukhov, 1954), one has to determine stability functions for momentum and heat which depend on a single stability parameter These stability functions must be determined empirically and have been obtained by different authors from regressions on observations from a small number of field experiments. The underlying non-linear equations must be solved iteratively at each time step of a model run which can be time consuming
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