# Hybrid Vertical Coordinate Testing and Evaluation

# Overview

The terrain-following sigma coordinate (Phillips, J. Meteor., 1957) has been implemented in many NWP systems including the Weather Research and Forecasting (WRF) model, and has been used with success for many years. However, a number of drawbacks are known to exist with this particular vertical coordinate. Due to the way that the horizontal component of the pressure gradient force is expressed in sigma coordinates, numerical truncation errors can occur over areas of steep terrain where coordinate surfaces depart significantly from a horizontal orientation. These errors then manifest as spurious horizontal and vertical accelerations in the model equations, often resulting in vertical columns of numerical noise in the model wind field (and other variables) over mountainous regions.

Given the impact these related errors can have on model variable accuracy and resulting forecasts (e.g., Park et al., Geophys. Res. Lett., 2016), a number of methods have been developed to mediate these problems. One such effort was undertaken by Joe Klemp of NCAR (2011, Mon. Wea. Rev.), with an eventual goal of adding this vertical coordinate option to WRF. In order to reduce some of the spurious horizontal and vertical accelerations associated with a pure terrain-following sigma coordinate, a smoothed, hybrid-coordinate was developed, in which the sigma coordinate is transitioned to a purely isobaric vertical coordinate at a specified level. Initial tests showed promising results for idealized cases with a considerable reduction in small-scale spurious accelerations. Based on these preliminary findings, the DTC was tasked with committing this new smoothed, hybrid coordinate option to the WRF repository, as well as testing and evaluation within both the RAP and HRRR in order to assess impacts on both retrospective cold-start and real-time forecasts.