Discovering New Representations of Near-Surface Exchange Using Symbolic Regression

Monin-Obukhov Similarity Theory (MOST) underpins most boundary layer flux estimates used in climate and weather simulation. MOST relies on several simplifying assumptions about the surface layer that are often incorrect, and, in practice, the empirically derived universal functions that are typically used poorly fit in-situ observations. This work uses a symbolic regression approach to discover new formulations for the universal functions. The method uses genetic optimization to discover new functional forms and gradient descent to tune their constants. New candidate formulations are identified that achieve lower error than existing empirically derived formulations when tested on a 6-year dataset of sonic anemometer observations from the 60-m mast at the ARM Southern Great Plains site. Finally, we apply the same approach to identify simple estimates of surface layer fluxes using dimensional values as inputs. The symbolic regression approach yields simple analytical solutions and avoids potential overfitting that can occur with large machine learning models.