Machine learning models for replacing Monin Obukhov similarity theory based surface layer parameterization

Flows in the atmospheric boundary layer (ABL) are turbulent, characterized by a large Reynolds number, the existence of a roughness sublayer, and the absence of a viscous layer. Exchanges with the surface are therefore dominated by turbulent fluxes. In numerical models for atmospheric flow, turbulent fluxes must be specified at the surface. Since surface fluxes are not known a priori they must be parameterized. When surface heat flux and vertical virtual potential temperature gradient both vanish, the structure of a neutrally stratified ABL is represented well by a logarithmic velocity profile. Due to diurnal variability and different atmospheric forcings the ABL structure is commonly affected by surface fluxes of heat and moisture. Under such conditions, velocity profiles deviate from a logarithmic structure.

Theoretical underpinning of the surface exchanges with the atmosphere were laid by Monin and Obukhov (1954). They developed a similarity theory linking measurements of wind speed and temperature at a level near the surface to the friction velocity and surface flux of sensible heat. Assuming that two relevant length scales (distance from the surface, z, and Obukhov length, L) account for the effect of a solid boundary and for competing effects of shear and buoyancy, Monin and Obukhov defined a non-dimensional stability parameter z/L. A number of field studies under nearly homogeneous and stationary conditions were carried out to determine universal stability functions that modify velocity and temperature profiles under non-neutral conditions. These stability functions are determined as simple linear and non-linear regression fits for stably stratified and unstable conditions, respectively. However, different regression parameters are obtained from different field studies (e.g., Businger et al. 1971, Dyer and Hicks 1970). Even when extreme care is taken to control the quality of the data, the scatter is large. Additionally, uncertainty emerges in parameters that are assumed to be constant, the von Karman constant and surface roughness length.

Nevertheless, in practice, these stability functions are commonly used even when the conditions of homogeneity and stationarity are not satisfied. Simple regression cannot capture the relationship between governing parameters and surface layer structure under the wide range of conditions to which Monin-Obukhov similarity theory (MOST) is commonly applied. We have therefore developed a machine learning model for an improved surface layer parameterization using long term surface layer observations.

To estimate surface fluxes of momentum, sensible heat, and moisture based on measurements of wind speed, temperature, humidity as well as surface temperature and soil moisture, we developed, trained, and tested two machine learning models. The machine learning models are based on the artificial neural network and random forest algorithms. To train and test these machine learning algorithms, we used several years of observations from the Cabauw mast in Netherlands and from the National Oceanic and Atmospheric Administration’s Field Research Division tower in Idaho.

Even when we train the machine learning models on one set of data and apply them to the second set, they provide more accurate estimates of all the fluxes than MOST. Estimates of sensible heat and moisture flux are significantly improved. We have now implemented the machine learning model based on the random forest algorithm in the Weather Research and Forecasting model. In this presentation, we demonstrate its performance in a single column model simulation based on the GABLES 2 model intercomparison study (Svensson et al. 2011).