Corona discharges are due to the ionization of the gas between two electrodes when the electric field near one of them is very strong. The lack of a complete understanding of the physical processes in negative corona discharge means that interest in corona discharge is still current. In this work, we use a more realistic hydrodynamic plasma model which considers 12 charged species such electron, ions, and molecules, with 32 chemical reactions present in the plasma and coupled with Helmholtz differential model to add effect of photoionization. The model is performed by needle-to-plane 2D- axisymmetric configuration and the digital algorithm based on the finite element method is implemented using the commercial software COMSOL Multiphysics (c). The aims of this work are to strengthen the understanding of negative corona discharge in air in a hydrodynamic plasma model. As well as to study the behavior of Trichel pulses when environmental parameters such as relative humidity, temperature, and pressure of the gas vary. Special attention is given when adding photoionization. The results of the numerical simulations show that the amplitude of the first Trichel pulse as well as the duration of the first pulse are strongly impacted by the variation of temperature, pressure, and relative humidity of environment gas. It is shown that the addition of photoionization has relatively impact on the results, especially with regard to the first Trichel pulse due to relative humidity which affects the ionization coefficient which in turn affects photoionization, what is needed for more realistic simulations.