The surface turbulent fluxes depend on the LSM, the atmospheric model and their coupling. Many studies already dealt with LSM evaluation predominantly offline (uncoupled mode – e.g., Chen et al., 1997; Boone et al. 2009, van den Hurk et al., 2011). Nearing et al (2018) concluded that surface fluxes over homogeneous surface are reasonably well simulated when the vegetation characteristics and the soil parameters and conditions are correctly set in the LSM. MOSAI will then consider that the soil and the vegetation schemes in LSM are indeed sufficiently accurate compared to the uncertainties related to the accounting for sub-grid heterogeneity. MOSAI objectives thus focus on the coupling between LSM and atmospheric models and its improvements (O3).

Over the last twenty years, the need to explore L-A interactions, and to improve our knowledge on involved processes and the performance of the models has emerged. In this context, many studies dealt with surface heterogeneities and their impact on secondary circulations and convection (field experiments: LITFASS (Beyrich and Mengelkamp 2006), International H20 Project (Weckwerth et al. 2004), SMACEX (Kustas et al. 2005); numerical studies: e.g., Kang (2009), Liu et al., 2011, Patton et al. 2005). Maronga and Raasch (2013) emphasized that the scale of the surface heterogeneities affecting the convective boundary-layer (CBL) changes in time during the day, with increasing CBL height. Secondary circulations induce horizontal transport from wet to dry area, trigger the convection (Courault et al., 2007; Taylor et al., 2012), and can contribute to 70% of the vertical flux (Patton et al., 2005). Most of these studies used surface patches with fixed flux or fixed temperature at surface to represent the surface heterogeneities. The MOSAI project, with coupled LSM-LES approach, will estimate the impact on L-A exchanges simulation of (1) secondary circulations, and, (2) realistic representation of the surface heterogeneity compared to surface percentages as used in ESM (O3).

The turbulent flux at surface in the atmosphere is estimated using bulk formulas based on the Monin Obukhov Similarity Theory (MOST). These formulas are applied whatever the mesh scale and the time step, from climate to LES models. The use of coupled LSM-LES is rather uncommon, and the few existing simulations show good results for the flux simulation (Patton et al., 2005; Lohou et al., 2014b; Brilouet et al., 2020). Coupled LSM-LES constitute an essential tool which fills the scale and temporal gaps between the local real-world measurement and the regional models. However, there are some limits of the LES tool concerning the L-A coupling. The MOSAI project will explore the relevance of bulk formulas for local and instantaneous (1 second) flux estimation in LES (O3) (Maronga et al., 2020).

The comparison between models and observations are often performed without taking into account the height of measurements and the vertical resolution of the models. The closer this height is to the surface the more the measurements are representative of a specific vegetation cover and consequently far from the heterogeneity integrated in the model grid cell. The higher the chosen level for the comparison, the more the measurement integrates the surface heterogeneity and tends towards the surface representation in the model (Bou-Zeid et al., 2004, 2007; Mason, P. J., 1988; Wieringa, J., 1986; Wood, N. and P. Mason, 1991). The MOSAI project will explore the vertical profile of the L-A exchanges according to the surface heterogeneities and meteorological conditions in the context of model-observation comparisons.

Current NWP and climate models couple the atmosphere with the land surface using several aproximations. While the land-surface component often treats several tiles (typically on the order of 10), which can strongly differ in terms of soil and vegetation properties depending on the subgrid-scale landscape, the atmosphere component considers a single atmospheric column forced by some average of the patch relevant fields (e.g., surface temperature and moisture, surface turbulent fluxes – André et al., 1986; Noilhan et al., 1997). Besides, even if the LSM treats them separately, the land-surface patches all see the same atmospheric column above, which thus strongly constrains the L-A coupling. The coupling between LSM and atmospheric models is then based on several approximations, which are different when considering LES, NWP or climate model. Among these: 1/ the consideration of the surface heterogeneity as a sum of different surfaces without considering heterogeneity scale and spatial distribution, 2/ a unique atmosphere for all the surfaces in the grid-mesh preventing interactions between the different surfaces and specific atmospheric columns, 3/ a unique aggregated flux as the lower atmospheric conditions preventing for the secondary circulation formation. These simplifications in the coupling between LSM and atmospheric models and their impacts on the simulated surface flux will be studied and quantified in the MOSAI project, and, a new coupling will be implemented and tested (O3).