I have some questions in Arithmetic Arakelov geometry

Let $\mathcal X\to Spec(\mathcal O_K)=C$ be an arithmetric projective variety over $C$ , where $\mathcal O_K$, ring of number filed $K$ and $\mathcal L$ be an arithmetic line bundle over $\mathcal X$ and $h$ be a positive Hermitian metric on $\mathcal L$,

Then

1- How can we compute the intersection number

$$(\overline{\mathcal L}^h)^n.(n+1)(\overline{K_{\mathcal X/C}}^{Ric(h)})$$

2.What is the definition of intersection number of two arithmetic line bundles

$$\overline{\mathcal L_1}.\overline{\mathcal L_2}$$

3.If we take $\mathcal D$ be an arithmetic divisor on $\mathcal X$, then how can we introduce $$\overline{\mathcal L_1}.\mathcal D$$