From AMS Glossary
A measure of the local spreading or divergence of a vector field in a horizontal plane, commonly written ∇H · V.
In Cartesian coordinates,
where u and v are the components of the vector field V along the horizontal axes x and y, respectively. The horizontal divergence of the velocity field is related to the vertical motion and local pressure variations through the equation of continuity and equations of motion. Horizontal divergence is often referred to simply as divergence.