The link between scalar second-order moments and gradient in the interfacial layer (IL) capping the convective boundary layer (CBL) is analysed using new lidar turbulent-scale observations. Temperature and moisture variances as well as sensible and latent heat fluxes have been measured during 100 hours in CBL temperate and arid regions with various free-cloud meteorological conditions. The IL fluxes and variances have been confronted with Lagrangian Stochastic Model (LSM) theories using scalar gradients, vertical velocity variance, kinetic energy dissipation rate and integral scales of turbulence with the purpose to build a local parametrization. The results show that a Pearson diffusion model in a stratified flow, that relies on the IL vertical velocity variance, and buoyant oscillation period, and 1 as the critical scale of turbulent diffusion, gives universal relevant parameters for IL temperature and moisture flux and variance. Our observations enable to infer for the first time IL local scaling for temperature, and moisture eddy diffusivities. The LSM local scaling parameters have been compared successfully for temperature with previous large-eddy simulations and with in-situ observations made in the nocturnal stratified atmospheric surface layer. Other LSM tested in this work that uses different scales to characterize IL scalar statistics, failed, especially for moisture statistics.