interesting regions.

Magnetic helicity and magnetic energy can be transported from the solar interior to the corona by the new emergence flux and the various motions of magnetic flux on the photosphere. The injection rate of the magnetic helicity across a surface S is expressed by [@ber84; @dem03; @par05]: $$\label{eq3}
   \dot H = 2\int_S(\textbf{A}_p\cdot \textbf{B}_t)V_{\bot n}dS - 2\int_s(\textbf{A}_p\cdot \textbf{V}_{\bot t})B_n dS,$$ where $\textbf{A}_p$ is the vector potential of the potential field $\textbf{B}_p$, $\textbf{B}_t$ and $\textbf{B}_n$ denote the tangential and normal magnetic fields, $\textbf{V}_{\bot t}$ and $V_{\bot n}$ are the tangential and normal components of the velocity perpendicular to the magnetic field lines, respectively. We derive the vector velocity field by using the Differential Affine Velocity Estimator for Vector Magnetograms (DAVE4VM) method [@sch08]. The first term contributed by the emerging flux tubes is named emergence term, and the second term generated by the shearing and braiding the field lines by the tangential motions is named shear term. Similarly, the rate of the magnetic energy (Poynting vector) can be derived by following equation [@kus02; @bi18]: $$\label{eq4}
    \dot E = \frac{1}{4\pi}\int _s B_t^2V_{\bot n}dS - \frac{1}{4\pi}\int_s(\textbf{B}_t \cdot \textbf{V}_{\bot t})B_ndS.$$ In the same way, the first term of the equation is named emergence term, 