Numerical Methods: The Arakawa Approach, Horizontal Grid, Global, and Limited-Area Modeling

Abstract Five sets of 48-h, 10-member, convection-allowing ensemble (CAE) forecasts with 3-km horizontal grid spacing were systematically evaluated over the conterminous United States with a focus on precipitation across 31 cases. The various CAEs solely differed by their initial condition perturbations (ICPs) and central initial states. CAEs initially centered about deterministic Global Forecast System (GFS) analyses were unequivocally better than those initially centered about ensemble mean analyses produced by a limited-area single-physics, single-dynamics 15-km continuously cycling ensemble Kalman filter (EnKF), strongly suggesting relative superiority of the GFS analyses. Additionally, CAEs with flow-dependent ICPs derived from either the EnKF or multimodel 3-h forecasts from the Short-Range Ensemble Forecast (SREF) system had higher fractions skill scores than CAEs with randomly generated mesoscale ICPs. Conversely, due to insufficient spread, CAEs with EnKF ICPs had worse reliability, discrimination, and dispersion than those with random and SREF ICPs. However, members in the CAE with SREF ICPs undesirably clustered by dynamic core represented in the ICPs, and CAEs with random ICPs had poor spinup characteristics. Collectively, these results indicate that continuously cycled EnKF mean analyses were suboptimal for CAE initialization purposes and suggest that further work to improve limited-area continuously cycling EnKFs over large regional domains is warranted. Additionally, the deleterious aspects of using both multimodel and random ICPs suggest efforts toward improving spread in CAEs with single-physics, single-dynamics, flow-dependent ICPs should continue.

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Dynamics of limited-area models: Formulation and numerical methods

Meteorology and Atmospheric Physics ◽

10.1007/bf01025360 ◽

1997 ◽

Vol 63 (1-2) ◽

pp. 3-14 ◽

Cited By ~ 21

Author(s):

F. Mesinger

Keyword(s):

Numerical Methods ◽

Limited Area

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Sensitivity of Limited-Area Hybrid Variational-Ensemble Analyses and Forecasts to Ensemble Perturbation Resolution

Monthly Weather Review ◽

10.1175/mwr-d-14-00259.1 ◽

2015 ◽

Vol 143 (9) ◽

pp. 3454-3477 ◽

Cited By ~ 23

Author(s):

Craig S. Schwartz ◽

Zhiquan Liu ◽

Xiang-Yu Huang

Keyword(s):

Hybrid Systems ◽

Hybrid System ◽

Wrf Model ◽

Limited Area ◽

Track Forecast ◽

Forecast Errors ◽

Grid Spacing ◽

Background Error ◽

Single Observation ◽

Horizontal Grid

Abstract Dual-resolution (DR) hybrid variational-ensemble analysis capability was implemented within the community Weather Research and Forecasting (WRF) Model data assimilation (DA) system, which is designed for limited-area applications. The DR hybrid system combines a high-resolution (HR) background, flow-dependent background error covariances (BECs) derived from a low-resolution ensemble, and observations to produce a deterministic HR analysis. As DR systems do not require HR ensembles, they are computationally cheaper than single-resolution (SR) hybrid configurations, where the background and ensemble have equal resolutions. Single-observation tests were performed to document some characteristics of limited-area DR hybrid analyses. Additionally, the DR hybrid system was evaluated within a continuously cycling framework, where new DR hybrid analyses were produced every 6 h over ~3.5 weeks. In the DR configuration presented here, the deterministic backgrounds and analyses had 15-km horizontal grid spacing, but the 32-member WRF Model–based ensembles providing flow-dependent BECs for the hybrid had 45-km horizontal grid spacing. The DR hybrid analyses initialized 72-h WRF Model forecasts that were compared to forecasts initialized by an SR hybrid system where both the ensemble and background had 15-km horizontal grid spacing. The SR and DR hybrid systems were coupled to an ensemble adjustment Kalman filter that updated ensembles each DA cycle. On average, forecasts initialized from 15-km DR and SR hybrid analyses were not statistically significantly different, although tropical cyclone track forecast errors favored the SR-initialized forecasts. Although additional studies over longer time periods and at finer grid spacing are needed to further understand sensitivity to ensemble perturbation resolution, these results suggest users should carefully consider whether SR hybrid systems are worth the extra cost.

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Deterministic Ensemble Forecasts Using Gene-Expression Programming*

Weather and Forecasting ◽

10.1175/2009waf2222192.1 ◽

2009 ◽

Vol 24 (5) ◽

pp. 1431-1451 ◽

Cited By ~ 32

Author(s):

Atoossa Bakhshaii ◽

Roland Stull

Keyword(s):

Gene Expression ◽

Fitness Function ◽

Gene Expression Programming ◽

Ensemble Forecast ◽

Ensemble Average ◽

Limited Area ◽

Ensemble Forecasts ◽

Weather Stations ◽

Mountain Weather ◽

Horizontal Grid

Abstract A method called gene-expression programming (GEP), which uses symbolic regression to form a nonlinear combination of ensemble NWP forecasts, is introduced. From a population of competing and evolving algorithms (each of which can create a different combination of NWP ensemble members), GEP uses computational natural selection to find the algorithm that maximizes a weather verification fitness function. The resulting best algorithm yields a deterministic ensemble forecast (DEF) that could serve as an alternative to the traditional ensemble average. Motivated by the difficulty in forecasting montane precipitation, the ability of GEP to produce bias-corrected short-range 24-h-accumulated precipitation DEFs is tested at 24 weather stations in mountainous southwestern Canada. As input to GEP are 11 limited-area ensemble members from three different NWP models at four horizontal grid spacings. The data consist of 198 quality controlled observation–forecast date pairs during the two fall–spring rainy seasons of October 2003–March 2005. Comparing the verification scores of GEP DEF versus an equally weighted ensemble-average DEF, the GEP DEFs were found to be better for about half of the mountain weather stations tested, while ensemble-average DEFs were better for the remaining stations. Regarding the multimodel multigrid-size “ensemble space” spanned by the ensemble members, a sparse sampling of this space with several carefully chosen ensemble members is found to create a DEF that is almost as good as a DEF using the full 11-member ensemble. The best GEP algorithms are nonunique and irreproducible, yet give consistent results that can be used to good advantage at selected weather stations.

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Comparing partial and continuously cycling ensemble Kalman filter data assimilation systems for convection-allowing ensemble forecast initialization

Weather and Forecasting ◽

10.1175/waf-d-21-0069.1 ◽

2021 ◽

Author(s):

Craig S. Schwartz ◽

Jonathan Poterjoy ◽

Jacob R. Carley ◽

David C. Dowell ◽

Glen S. Romine ◽

...

Keyword(s):

Kalman Filter ◽

Data Assimilation ◽

Ensemble Kalman Filter ◽

Limited Area ◽

Computational Domain ◽

Grid Spacing ◽

Pass Filter ◽

Continuous Cycling ◽

Horizontal Grid ◽

Better Than

AbstractSeveral limited-area 80-member ensemble Kalman filter (EnKF) data assimilation systems with 15-km horizontal grid spacing were run over a computational domain spanning the conterminous United States (CONUS) for a 4-week period. One EnKF employed continuous cycling, where the prior ensemble was always the 1-h forecast initialized from the previous cycle’s analysis. In contrast, the other EnKFs used a partial cycling procedure, where limited-area states were discarded after 12 or 18 h of self-contained hourly cycles and re-initialized the next day from global model fields. “Blended” states were also constructed by combining large scales from global ensemble initial conditions (ICs) with small scales from limited-area continuously cycling EnKF analyses using a low-pass filter. Both the blended states and EnKF analysis ensembles initialized 36-h, 10-member ensemble forecasts with 3-km horizontal grid spacing. Continuously cycling EnKF analyses initialized ~1–18-h precipitation forecasts that were comparable to or somewhat better than those with partial cycling EnKF ICs. Conversely, ~18–36-h forecasts with partial cycling EnKF ICs were comparable to or better than those with unblended continuously cycling EnKF ICs. However, blended ICs yielded ~18–36-h forecasts that were statistically indistinguishable from those with partial cycling ICs. ICs that more closely resembled global analysis spectral characteristics at wavelengths > 200 km, like partial cycling and blended ICs, were associated with relatively good ~18–36-h forecasts. Ultimately, findings suggest that EnKFs employing a combination of continuous cycling and blending can potentially replace the partial cycling assimilation systems that currently initialize operational limited-area models over the CONUS without sacrificing forecast quality.

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