  This paper examines the application of adaptive mesh refinement (AMR) in the
field of numerical weather prediction (NWP). We implement and assess two
distinct AMR approaches and evaluate their performance through standard NWP
benchmarks. In both cases, we solve the fully compressible Euler equations,
fundamental to many non-hydrostatic weather models.
  The first approach utilizes oct-tree cell-based mesh refinement coupled with
a high-order discontinuous Galerkin method for spatial discretization. In the
second approach, we employ level-based AMR with the finite difference method.
Our study provides insights into the accuracy and benefits of employing these
AMR methodologies for the multi-scale problem of NWP. Additionally, we explore
essential properties including their impact on mass and energy conservation.
Moreover, we present and evaluate an AMR solution transfer strategy for the
tree-based AMR approach that is simple to implement, memory-efficient, and
ensures conservation for both flow in the box and sphere.
  Furthermore, we discuss scalability, performance portability, and the
practical utility of the AMR methodology within an NWP framework -- crucial
considerations in selecting an AMR approach. The current de facto standard for
mesh refinement in NWP employs a relatively simplistic approach of static
nested grids, either within a general circulation model or a separately
operated regional model with loose one-way synchronization. It is our hope that
this study will stimulate further interest in the adoption of AMR frameworks
like AMReX in NWP. These frameworks offer a triple advantage: a robust dynamic
AMR for tracking localized and consequential features such as tropical
cyclones, extreme scalability, and performance portability.
