  Some types of coupled Korteweg de-Vries (KdV) equations are derived from an
atmospheric dynamical system. In the derivation procedure, an unreasonable
$y$-average trick (which is usually adopted in literature) is removed. The
derived models are classified via Painlev\'e test. Three types of
$\tau$-function solutions and multiple soliton solutions of the models are
explicitly given by means of the exact solutions of the usual KdV equation. It
is also interesting that for a non-Painlev\'e integrable coupled KdV system
there may be multiple soliton solutions.
