A top sublayer with forced convection and a fixed bottom boundary was identified in the convective atmospheric surface layer. “Linear” approximations were shown to be effective for the description of second turbulent moments in this sublayer. These approximations correspond to truncated Taylor expansions with respect to inverse dimensionless height, in which only two terms are retained. The first terms in the expansion do not take wind into account and correspond to the limiting relationships of Monin–Obukhov similarity theory in the regime of free convection. The second terms of the expansion take into account wind and its effect on convection. The existence of the sublayer of forced convection with a fixed boundary leads to the construction of a one-parameter family of analytical approximations of turbulent moments depending on the elevation of the bottom boundary of this sublayer. The proposed approximations of the variances of vertical velocity, fluctuations of temperature, fluctuations of humidity, and fluctuations of carbon dioxide are compared with the available experimental data over both water surface and land surface.