Effects of coarsely resolved and temporally interpolated lateral boundary conditions on the dispersion of limited-area ensemble forecasts

This work examines the impact of coarsely resolved and temporally interpolated lateral boundary conditions (LBCs) on the dispersion of limited-area-model (LAM) ensemble forecasts. An expression is developed that links error variance spectra to ensemble spread while accounting for spatial and ensemble mean effors. The balances required by this expression are used to show that LBC constraints on small-scale error variance growth are sufficient to help cause underdispersive LAM ensemble simulations. The hypothesis is tested in a controlled and efficient manner using a modified barotropic channel model. Ten-member ensemble simulations are produced over many cases on a "global" periodic channel domain and each of four smaller nested LAM domains. Lateral boundary effects are specifically isolated since all simulations are perfect except for initial condition perturbations and the use of coarsely resolved and/or temporally interpolated "one-way" LBCs. This configuration excludes other analysis and external model system errors that are not caused directly by the implementation of LBCs. Statistical results accumulated over 100 independent cases demonstrate that LAM ensembles remain underdispersive even when using a complete set of LBCs from an external ensemble forecast. The small-scale constraints on error growth are present in any modeling system using coarsely resolved or temporally interpolated one-way LBC forcing. Although not tested here, similar limitations may apply to global variable-resolution models because of insufficient small-scale variance outside the perimeter of higher-resolution subdomains. The results of this work suggest the need to apply statistically consistent, small-scale LBC perturbations at every time step throughout the LAM simulations.