  In this paper, we will study the asymptotic geometry of 4-dimensional steady
gradient Ricci solitons under the condition that they dimension reduce to
$3$-manifolds. We will show that such 4-dimensional steady gradient Ricci
solitons either dimension reduce to a spherical space form
$\mathbb{S}^3/\Gamma$ or weakly dimension reduce to the $3$-dimensional Bryant
soliton. We also show that 4-dimensional steady gradient Ricci soliton
singularity models with nonnegative Ricci curvature outside a compact set
either are Ricci-flat ALE $4$-manifolds or dimension reduce to $3$-dimensional
manifolds. As an application, we prove that any steady gradient
K\"{a}hler-Ricci soliton singularity models on complex surfaces with
nonnegative Ricci curvature outside a compact set must be hyperk\"{a}hler ALE
Ricc-flat $4$-manifolds.
