A mesoscale planetary boundary layer (PBL) numerical model has been developed to study airflow over complex topography. Turbulence closures using the turbulent kinetic energy (TKE) and dissipation (ε) equations are investigated in combination with the level 2.5 scheme of Mellor and Yamada (1982) to determine eddy diffusivities for momentum and heat. This modified E-ε closure is simpler than the level 3 one which requires more prognostic equations for moist turbulent transport. One-dimensional (1-D) model results show that the PBL mean flows under various stability conditions are not significantly sensitive to the modified Blackadar and Kolmogorov eddy mixing-length formulations used in this E-ε model, although the latter yields excessively large mixing lengths in the entrainment region of the upper PBL. Eddy mixing lengths in the Kolmogorov-type formulation can be better defined by introducing background dissipation. Using the same prognostic TKE equation, the 1-D model results are not significantly affected by different diagnostic formulations in the closures. The simulated results compare well with large-eddy simulations and those obtained using higher-order closure schemes including the level 3 one. The results are found to be insensitive to eddy Prandtl number, in contrast to the 2-D model results (see Part II).