Fig. 2

Schematic showing gridded data structure and numerical approximations used for moisture budget diagnostics. The ERA5moistIN dataset incorporates atmospheric variables (e.g., wind, humidity, pressure) on a 3D grid spanning multiple pressure levels and hourly time steps. The central 3D view shows the vertical structure used for computing vertical gradients and fluxes. The top-right horizontal grid highlights how finite-difference approximations are applied at each level to estimate horizontal derivatives. The red box marks a representative grid point (i,j,k) at time t, where specific moisture budget terms such as advection, convergence, and flux divergence are evaluated. Central differences are used for interior points, while forward and backward differences are applied at boundaries. Horizontal grid spacing is converted from latitude–longitude coordinates to metric distances, with curvature corrections included for vector derivatives. This framework enables consistent computation of key moisture budget components, including horizontal and vertical advection, wind convergence, and moisture flux convergence.