## 1 Introduction
The reaction of NO and O\({}_{3}\) in the atmosphere should consider the effect of turbulence with D\({}_{t}\geq 1\) when the intensity of segregation is always negative in the situation where both species are introduced at opposite boundaries [10]. Large regional ozone studies have been carried out in the San Joaquin Valley (central California) [11], Southeastern United States [12; 13; 14; 15], Lake Michigan [16], Northeastern United States [17; 18], United States [19; 20], eastern North America [21], Russia [22], and Australia [23]. In those areas, maximum ozone concentrations during the summer exceeded the O\({}_{3}\) national ambient air quality standard (NAAQS) of 70 ppb finalized by the USEPA in 2015. Ozone studies have led to the recognition that realistic representations of turbulent mixing processes are very important for air quality simulation. The effects of incomplete mixing on the chemical reaction between two species such as NO and O\({}_{3}\) are potentially very important when the time scale of the chemical reaction is of the same order or faster than the turbulent time scale [3; 4; 5; 6; 7; 8; 10]. A 1-D Turbulent Kinetics Model (TKM) [10] is applied to study the NO\({}_{x}\)-O\({}_{3}\) cycle as a representative reaction system whose reaction rates are affected by turbulent mixing in the convective boundary layer (CBL). The TKM chemical kinetics expression is modified by a term containing the covariance of the reactant concentrations in order to account for the effects of turbulence. Other studies have extended the scope to a more complex chemistry mechanism containing a wide range of chemical time scales [24; 25; 26]. The vertical turbulent transport of trace reactive species (the O\({}_{3}\)-NO-NO\({}_{2}\) triad) in the CBL during daytime has been used in the Second-Order Model for Conserved and Reactive Unsteady Scalars (SOMCRUS)[24]. SOMSCRUS [27; 28] is run to investigate reactive species in the CBL and to obtain continuous equilibrium profiles of turbulent fluxes and mean concentrations of reactive scalars (the O\({}_{3}\)-NO-NO\({}_{2}\) triad) in a steady-state CBL without shear [29]. Also, SOMCRUS is used to calculate time-varying continuous profiles of mean concentrations and vertical turbulent fluxes, variances and covariances of both passive and reactive scalars (the O\({}_{3}\)-NO-NOtriad) [24]. A system in a simulation with a 1-D coupled diffusion and chemistry model applies a second-order closure scheme in the neutral Atmospheric Boundary Layer (ABL) over a remote deciduous forest [26]. However, those studies used the mean reaction rate formulation of the chemical kinetics which neglected the contribution of the covariance term. The turbulent effect on chemical reaction rates has been studied for \"essential\" daytime photochemistry with hydrocarbons and with various chemical time scales in the CBL by means of a large eddy simulation (LES)[25]. Those results showed that turbulence played a relatively modest role in affecting the evolution of the reaction system. The present study has an originality to develop the computational turbulent kinetic model (TKM) for expressing nonlinear kinetics and dynamics of chemicals in heterogeneous systems. For validating TKM applicability, model simulations are run for essential NO\({}_{\text{x}}\)-O\({}_{3}\)-RH photochemistry in a convective boundary layer (CBL). The present study uses the turbulent kinetics model (TKM) [10] and a set of photochemical reactions [25] to simulate the effects of turbulence on the reaction rates and distribution of important species in the CBL. For this purpose, this study compare the TKM results to those of a box model (BM), a conventional kinetics model (CKM) and the LES model [25]. Also, this study aims at providing the results of a sensitivity analysis of the TKM to show the effects of changes in such important parameters as nitric oxide (NO) and hydrocarbon (HC or RH) emission rates, reaction rate constants, dry deposition velocity, exchange velocity, turbulent time scale, and initial concentrations of species.