Modeling turbulence is an important object of environmental sciences for describing an essential turbulent transport of heat and momentum in the boundary layer of the atmosphere. The many turbulence model used in the simulation of flows in the environment, based on the concept of eddy viscosity, and buoyancy effects are often included in the expression for the turbulent fluxes through empirical functions, based on the similarity theory of Monin-Obukhov, fair, strictly speaking, only in the surface layer. Furthermore, significant progress has been made in recent years in the development broader than standard hypothesis turbulent viscosity models for the eddy diffusivity momentum and heat, as a result of the recording of differential equations for the Reynolds stresses and vector turbulent heat flux in a weakly-equilibrium approximation, which neglects advection and the diffusion of certain dimensionless quantities. Explicit algebraic model turbulent Reynolds stresses and heat flux vector for the planetary boundary layer is tested in the neutral atmospheric boundary layer over the homogeneous rough surface. The present algebraic model of turbulence built on physical principles RANS (Reynolds Average Navier Stokes) approach for stratified turbulence uses three prognostic equations and shows correct reproduction of the main characteristics of the Ekman neutral ABL: the components average of wind velocity, the angle of wind turn, turbulence statistics. Test calculations shows that this turbulence model can be used for the purposeful researches of the atmospheric boundary layer for solving of various problems of the environment.