Abstract The minimum number of members in a numerical weather prediction ensemble has long been debated. In this study, we estimate the minimum ensemble size ( N min ) for prediction of temperature, precipitation, and snow water equivalent for the 200-member regional weather model West-WRF ensemble for the winter (December-March) 2021–2022. We give examples of how to estimate N min for three skill metrics by finding the number of ensemble members needed to reduce the relative difference in mean skill score from that of the full ensemble or to reduce the spread of the skill score to a certain threshold depending on the skill score. N min estimates are found when the relative difference in skill reduces to two different sample thresholds. The less stringent threshold N min for deterministic and probabilistic skill (~20–30) is similar to the size of ensembles currently produced at operational centers. There is a smaller difference between the less and more stringent threshold N min to account for sampling uncertainty. N min based on all metrics shows some sensitivity to whether an atmospheric river is landfalling. A simple post-processing scheme minimizing biases and leveraging persistence was used to test sensitivity of N min to bias correction. The most sensitivity was shown for snow water equivalent resulting in a reduction in the difference between the two thresholds for sampling uncertainty.
Abstract Most studies on meso-convective systems have identified favorable atmospheric conditions through subjective analysis of deterministic outputs or selected ensemble members. In contrast, this study applies three objective data analysis methods to 1000-member ensemble simulations of the July 2020 Kyushu heavy rainfall event: ensemble sensitivity analysis (ESA), partial least squares (PLS), and, for the first time in ensemble-based sensitivity analysis, generative topographic maps (GTM), a nonlinear machine-learning method. The large ensemble size permits these analyses without localization, preserving physically meaningful remote correlations. All three methods converge on a consistent mechanism: heavy rainfall is most sensitive to a deepened Baiu frontal depression west of Kyushu with enhanced low-level moisture flux from the west rather than the southwest. The GTM analysis adds what the linear methods cannot provide: the full range of scenarios present in the ensemble, and the critical differences between the favorable and the unfavorable configurations. The convergence of linear and nonlinear methods provides robust, objective validation of the identified mechanism, while demonstrating the potential of machine-learning approaches for ensemble-based sensitivity analysis.
Abstract Land surface characteristics such as soil moisture can influence convection initiation (CI) along the Great Plains dryline, while convective precipitation itself influences soil moisture. Therefore, land–atmosphere strongly coupled data assimilation (SCDA) is particularly attractive in the context of dryline CI events. However, effective convective-scale ensemble-based SCDA requires a better understanding of the characteristics of the coupled-correlation structure associated with land surface uncertainty and the sampling error associated with ensemble-based estimates of that coupled-correlation structure. Herein, a dryline CI case study shows that the coupled correlations between land and atmosphere variables are particularly pronounced along the dryline, in the vicinity of the subsequent CI. While this study does not attempt to provide a fully optimized estimate of the coupled background error covariance or the optimal localization length scales, some guidance for future development of convective-scale land–atmosphere SCDA can be inferred. Quantitatively, this study suggests that smaller horizontal localization length scales are likely optimal for soil variables than for atmosphere thermodynamic variables for a given ensemble size. Additionally, smaller ensembles (in this case, ∼60 members) are likely sufficient for land–atmosphere coupled correlations involving soil temperature but larger ensembles (in this case, ∼100–200 members) are likely needed to reliably estimate the sign of the coupled correlations involving soil moisture. Qualitatively, this study also suggests that treatments of sampling error that are not distance based are likely necessary during convective-scale SCDA to mitigate the sampling error that dominates across much of the domain while still retaining the part of the ensemble-based cross-component correlation that would be expected to improve dryline CI analyses and forecasts.
Abstract A positivity-preserving limiter is presented for the discontinuous Galerkin (DG) transport scheme on the cubed-sphere, with non-conforming adaptive mesh refinement capability. The limiter is based on a flux-corrected transport method as used in numerous finite-volume transport models. Recently, such a limiter has been developed for the DG discretization of the linear advection equation in two-dimensional Cartesian geometry, known as the “truncated mass aware rescaling”, which has been shown to be high-order accurate. The flux-correction procedure associated with the limiter ensures element-wise mean mass to be non-negative, followed by a rescaling step which enforces the grid-point values of the scalar field in the element remain positive-definite, using the local mass-conservation constraints. In the present work, the limiter is further extended to the spherical geometry employing curvilinear cubed-sphere grid with non-conforming elements. The DG flux exchange between the non-conforming coarse and fine elements at the interfaces is constrained to be conservative by an integral projection method. The application of the limiter to the non-conforming elements is consistent with the mesh geometry, where each element is treated as a finite-volume cell with the same mass. Numerical results with solid-body rotation and deformational-flow test cases show that the limiter maintains the high-order accuracy of the DG scheme while remaining positivity-preserving and mass-conservative.
Abstract A proper localization length scale is critical for the success of ensemble-based data assimilation techniques to reduce spurious, long-distance correlations that stem from limited ensemble size. This study utilizes 960-member ensemble forecasts from the Global Ensemble Forecast System (GEFS) to examine the structures of the correlations for the planetary boundary layer (PBL) height (PBLH). Results show that the autocorrelation of PBLH decreases exponentially with increasing separation distance, with an average e-folding distance of 150–400 km. Diurnal cycles, seasons, synoptic-scale weather systems, and other land and atmosphere conditions modulate the autocorrelation scale, with autocorrelation scales being broader and having less diurnal and seasonal variations over sea than over land. Soil temperature and soil moisture show strong positive and negative cross-correlations with PBLH, respectively. These cross-correlations have notable diurnal cycles that yield the strongest correlations during early afternoon, and the magnitudes of the correlations decrease rapidly with increasing soil depths. There are also strong cross-correlations between PBLH and temperature and moisture within the PBL. These cross-correlations exhibit dependence on the diurnal cycle with magnitudes peaking in the early afternoon, and strong cross-correlations generally extend throughout the entire PBL during daytime. These characteristics are consistent with our physical understanding of the land-atmosphere interaction and the PBL, and the correlation structures can help the design of horizontal and vertical localizations when assimilating PBLH observations.
