# On consequences of measurements of turbulent Lewis number from observations

## TL;DR

This paper investigates the turbulent Lewis number derived from observations, proposing a new entropy-based coefficient and showing that its values often differ from unity, which impacts turbulence flux calculations in weather and climate models.

## Contribution

It introduces a new entropy-based exchange coefficient for moist air and demonstrates that the entropy Lewis number often deviates from one, challenging common assumptions in turbulence parameterizations.

## Key findings

- Le_ts values often differ significantly from 1
- Using entropy-based coefficients affects turbulence flux calculations
- Observations and models show large variability in Le_ts

## Abstract

Almost all parameterizations of turbulence in NWP models and GCM make the assumption of equality of exchange coefficients for heat $K_h$ and water $K_w$. However, large uncertainties exists in old papers published in the 1950s, 1960s and 1970s, where the turbulent Lewis number Le_t $= K_h / K_w$ have been evaluated from observations and then set to Le_t$=1$. The aim of this note is: 1) to trust the recommendations of Richardson (1919), who suggested to use the moist-air entropy as a variable on which the turbulence is acting; 2) to compute a new exchange coefficients $K_s$ for the moist-air entropy; 3) to determine the values of the new entropy-Lewis number Le_ts $= K_s / K_w$ from observations (M\'et\'eopole-Flux and Cabauw masts) and from LES and SCM outputs for the IHOP case (Couvreux et al., 2005). It is shown that values of Le_ts significantly different from $1$ are frequently observed and may have large consequences on the way the turbulence fluxes are computed in NWP models and GCMs.