Machine Learning for Improving Surface-Layer-Flux Estimates

Abstract

Flows in the atmospheric boundary layer are turbulent, characterized by a large Reynolds number, the existence of a roughness sublayer and the absence of a well-defined viscous layer. Exchanges with the surface are therefore dominated by turbulent fluxes. In numerical models for atmospheric flows, turbulent fluxes must be specified at the surface; however, surface fluxes are not known a priori and therefore must be parametrized. Atmospheric flow models, including global circulation, limited area models, and large-eddy simulation, employ Monin–Obukhov similarity theory (MOST) to parametrize surface fluxes. The MOST approach is a semi-empirical formulation that accounts for atmospheric stability effects through universal stability functions. The stability functions are determined based on limited observations using simple regression as a function of the non-dimensional stability parameter representing a ratio of distance from the surface and the Obukhov length scale (Obukhov in Trudy Inst Theor Geofiz AN SSSR 1:95–115, 1946), $$z/L$$ z / L . However, simple regression cannot capture the relationship between governing parameters and surface-layer structure under the wide range of conditions to which MOST is commonly applied. We therefore develop, train, and test two machine-learning models, an artificial neural network (ANN) and random forest (RF), to estimate surface fluxes of momentum, sensible heat, and moisture based on surface and near-surface observations. To train and test these machine-learning algorithms, we use several years of observations from the Cabauw mast in the Netherlands and from the National Oceanic and Atmospheric Administration’s Field Research Division tower in Idaho. The RF and ANN models outperform MOST. Even when we train the RF and ANN on one set of data and apply them to the second set, they provide more accurate estimates of all of the fluxes compared to MOST. Estimates of sensible heat and moisture fluxes are significantly improved, and model interpretability techniques highlight the logical physical relationships we expect in surface-layer processes.

On the Application of an Observations‐Based Machine Learning Parameterization of Surface Layer Fluxes Within an Atmospheric Large‐Eddy Simulation Model

“…Herein we have provided a general overview of the NN models across the range of observed conditions. The reader is referred to McCandless et al (2022) for a more detailed evaluation of the skill of ML models versus MOST, including the specific performance under the different stability regimes. theory was developed for mean quantities, it is the standard practice in LES of atmospheric flows to apply it irrespective of the grid size (e.g., Beare et al, 2006;Moeng, 1984), in lack of a universally agreed upon improved parameterization of surface-layer fluxes that is based on instantaneous fields to date.…”

“…These investigations proved to illustrate the importance in careful selection of the input predictors to the NN model. As already discussed, the ML models developed and exercised herein differ from those of McCandless et al (2022) in that we have used a reduced number of predictors (4 instead of 16). Moreover, these predictors are expressed in the form of vertical gradients (implied in the case of wind speed which vanishes at the surface) improving the generalizability of the model.…”

“…The reader is referred to McCandless et al. (2022) for a more detailed evaluation of the skill of ML models versus MOST, including the specific performance under the different stability regimes.…”

“…That is the work by McCandless et al. (2022), which addresses the problem of improving estimation of surface‐layer turbulent fluxes versus the scientific standard and broadly adopted Monin − Obukhov (MO) similarity theory (Monin & Obukhov, 1954), typically used as bottom boundary conditions in atmospheric models (e.g., A. Beljaars & Holtslag, 1991; Jiménez et al., 2012). McCandless et al.…”

“…Beljaars & Holtslag, 1991;Jiménez et al, 2012). McCandless et al (2022) use random forests (RF) and artificial neural network (NN) machine learning models to provide improved estimates of momentum, heat and moisture surface fluxes when compared to tower observations versus the state-of-the-art MO theory estimates mimicking its implementation in atmospheric models. This effort demonstrates the potential of ML models to overcome some of the limitations related to the simple regression fits employed to determine the stability correction parameter (only a function of the inverse Obukhov length) and other limitations inherent to the MO formulation of surface-layer fluxes (e.g., assumed homogeneous and stationary conditions).…”