The Influence of Vertical Advection Discretization in the WRF-ARW Model on Capping Inversion Representation in Warm-Season, Thunderstorm-Supporting Environments

Previous research has identified shortcomings in capping inversion representations within short-range Advanced Research Weather Research and Forecasting (WRF-ARW) model forecasts. In specific, WRF-ARW–modeled capping inversions are not as well-resolved as their counterparts in both observations and other models such as the Met Office’s Unified Model. Since convection-allowing guidance used by the Storm Prediction Center is primarily obtained using WRF-ARW, these shortcomings constrain deterministic and ensemble numerical forecast skill. Physically, poor inversion representation impacts inversion strength and depth; derived thermodynamic parameters such as CAPE, CIN, B_min, and boundary layer depth; dryline propagation; and convection initiation and severity. While it would be natural to ascribe these shortcomings to planetary boundary layer parameterization or vertical grid spacing, several investigations suggest that these are not leading contributions to poor WRF-ARW–modeled inversion representations.

In WRF-ARW, partial derivatives are computed using finite difference approximations; the default formulations are fifth- and third-order-accurate for horizontal and vertical advection, respectively. The third- and fifth-order accurate formulations are associated with implicit damping, preferentially of short wavelength features. By contrast, the Unified Model uses semi-Lagrangian spatial differencing that does not implicitly damp. Likewise, even-order-accurate formulations do not implicitly damp and are also slightly more accurate than their corresponding next-lower-order-accurate formulation, but have modestly more restrictive numerical stability criteria (potentially resulting in the need for a longer time step) and are numerically dispersive.

As vertical motion is a primary control on inversion strength, we hypothesize that model-derived vertical profiles will be more skillful in capping inversion environments within numerical simulations using the fourth- (rather than third-) order-accurate vertical advection finite difference formulation due to the latter’s preferential implicit damping of shorter wavelength features. To test this hypothesis, two parallel short-range (0-24 h) convection-allowing forecasts are run daily at 0000 UTC during the 2017 Hazardous Weather Testbed Spring Forecasting Experiment, one each in which third- and fourth-order-accurate vertical advection finite difference formulations are used. Model-forecast vertical profiles and derived thermodynamic instability parameters at 1200 UTC and 0000 UTC are verified against observations at locations in the ‘general thunderstorm’ contour from the 0600 UTC Storm Prediction Center Day 1 Convective Outlook. Results are separated into inversion and no inversion composites for focused testing of the motivating hypothesis.