Ultimately, the true strength of SHiELD is that all of these characteristics are demonstrated in the same modeling system.
SHiELD is designed to be an experimental research modeling system, with a particular set of scientific goals set by its developers, and thereby is more restricted in scope than the GFS, HAFS, RFS, and other general-purpose models intended for operational weather forecasting and to support broad audiences of users. While improved prediction skill is a major scientific goal and an important “vital sign” of model development, we also develop SHiELD as a means to demonstrate new modeling capabilities. SHiELD is also intended to be principally a physical atmosphere modeling system and is not intended for research into oceanic dynamics, decadal-to-centennial projection, biogeochemistry, or other topics taking place at either longer timescales or greater complexity than SHiELD is designed for. Improvements within SHiELD can be seamlessly transitioned into other FV3-based models that do address these topics, including other Unified Forecast System models and the FV3-based coupled earth-system models at GFDL, within NASA, NCAR, and elsewhere. As such SHiELD’s progress will continue to contribute to the development and improvement of these modeling systems. SHiELD is a part of GFDL’s fourth-generation modeling suite (GFDL 2019, Figures 1 and 2) and shares common infrastructure with CM4, ESM4, and SPEAR. SHiELD uses a different physics suite and land model from the other GFDL configurations, but otherwise is constructed similarly. Advances can then be exchanged between the configurations, allowing for mutual improvement, seamless cross-timescale modeling, and potentially unification of GFDL’s weather and climate modeling efforts. A significant two-way interaction between SHiELD and other UFS configurations (GFS, HAFS, RFS, etc.) is taking and promises to continue driving furthered improvement of all UFS applications.
Further development of SHiELD, including both FV3 and the SHiELD physics, will continue to improve the prediction skill of the configurations, address issues which have been identified, and broaden the scope towards new applications. As computing power allows, models will be pushed to higher horizontal and vertical resolution, physical processes developed to improve simulation quality and prediction skill, and to address emerging scientific questions. New capabilities within FV3, including regional and doubly periodic domains, will permit efficient simulation of processes at kilometer and sub-kilometer scales for basic science and for process studies to improve physical parameterizations. We are also working on a native SHiELD data assimilation cycling system to take advantage of the new advances and to create initial conditions most consistent with the forward prediction model configurations. Finally, development will continue of our Tier-2 configurations, with near real-time S2S predictions being made using S-SHiELD, and continued extension into the global cloud-resolving regime (cf. Stevens2019) towards new scientific problems not adequately addressed by existing regional models or by coarse-resolution global models.
Acknowledgments
SHiELD grew out of a major collaboration between GFDL and EMC and would not have been possible without the physical parameterization suite, software, data, and especially input initial conditions and baseline forecasts made freely available by EMC and the National Weather Service. We thank Jongil Han for providing SA-SAS, and George Gayno and Helin Wei for providing EMC pre-processing tools and land model inputs and for significant assistance with these tools and datasets. We also thank James Franklin (NHC, retired) for advice on the accuracy of the wind radii in the best-track dataset. Kate Zhou and Tom Delworth provided reviews of this manuscript. Xi Chen, Linjiong Zhou, Kun Gao, Yongqiang Sun, Kai-Yuan Cheng, and Morris Bender are funded under award NA18OAR4320123 from the National Oceanic and Atmospheric Administration, U.S. Department of Commerce. Xi Chen, Zhou, and Cheng were additionally funded by the Next-Generation Global Prediction System project of the National Weather Service. The National Oceanic and Atmospheric Administration’s Hurricane Supplemental Program Office partially funded Zhou, Gao, and Bender under award NA19OAR0220147; Sun under NA19OAR0220145; and Cheng under NA19OAR0220146. Supporting data can be found at doi:10.5281/zenodo.3997344. We thank two anonymous reviewers for their insightful comments.
Appendix A: Positive-Definite Advection Scheme
The Lagrangian dynamics in FV3 uses 1D advection operators to build the 2D advection scheme of Lin and Rood (1996). In hydrostatic FV3 these operators are typically monotonic (Lin 2004), in that no new extrema are created by the advection; however monotonic advection can be overly diffusive for some applications. In nonhydrostatic FV3 the monotonicity constraint is not used for advection of dynamical quantities (vorticity, heat, air mass), but positivity still needs to be enforced for scalar tracers. We introduce a positive-definite scheme, which uses a weaker constraint than monotonicity which only prevents the appearance of negative values.
This positivity constraint can be applied to any scheme similar to VanLeer (1974) or PPM (Collella and Woodward 1984) in which first-guess continuous edge values \({\hat{q}}_{i+1/2}\ \)and\({\hat{q}}_{i-1/2}\) are interpolated from the cell-averaged values\(\overline{q_{i}}\) where i is a grid index. As with a standard monotonicity constraint we break the continuity of the sub-grid reconstructions across grid-cell interfaces, creating left-edge and right-edge values, \(Q_{i}^{-}\) and \(Q_{i}^{+}\), respectively, as well as a curvature value \(B_{\text{oi}}\) for each grid cell, which are then used to compute the flux as in Putman and Lin (2007), Appendix B.
To adjust the edge values to ensure positivity, we use the algorithm below on cell i , where notation is as in Lin (2004), Appendix A:
\(Q_{i}^{-}\) = \({\hat{q}}_{i-1/2}\)- \(\overline{q_{i}}\)
\(Q_{i}^{+}\)= \({\hat{q}}_{i+1/2}\)- \(\overline{q_{i}}\)
\(B_{\text{oi}}\)=\(\ Q_{i}^{-}\) + \(Q_{i}^{+}\)
\(\Delta A_{i}\) = \(Q_{i}^{+}\)- \(Q_{i}^{-}\)
\(A_{4i}\) = -3 \(B_{\text{oi}}\)
If abs(\({\hat{q}}_{i+1/2}\)-\({\hat{q}}_{i-1/2}\)) > -\(A_{4i}\) and \(\overline{q_{i}}\)+\(\Delta{A_{i}}^{2}\)/\(\left(4A_{4i}\right)\) +\(\frac{1}{12}A_{4i}\) < 0 then
If \(Q_{i}^{-}Q_{i}^{+}\) > 0 then
\(Q_{i}^{-}\) = \(Q_{i}^{+}\) = \(B_{\text{oi}}\) = 0
Elseif dAi > 0 then
\(Q_{i}^{+}\)= -2*\(Q_{i}^{-}\)
\(B_{\text{oi}}\) = -\(Q_{i}^{-}\)
Else
\(Q_{i}^{-}\)= -2*\(Q_{i}^{+}\)
\(B_{\text{oi}}\) = -\(Q_{i}^{+}\)
Appendix B: Split and In-line GFDL Microphysics
The GFDL microphysics, a single-moment six-category microphysics, has its origin in the microphysics of Lin et al. (1983) as implemented within GFDL ZETAC (Pauluis and Garner, 2006; Knutson et al., 2007, 2008) with further developments from Lord et al. (1984) and Krueger et al. (1995). It was later substantially revised for use in HiRAM (Chen and Lin, 2011, 2013; Harris et al., 2016; Gao et al., 2017, 2019) by adding the following updates:
  1. Time-splitting is applied between warm-rain and ice-phase processes, with the warm-rain processes called twice per invocation.
  2. PPM is applied for sedimentation of all condensate species except cloud water, ensuring shape preservation and stability.
  3. The heat content of condensates is included when heating/cooling grid cells.
  4. Scale awareness is achieved by assuming a horizontal subgrid distribution and a second-order vertical reconstruction for autoconversion processes with a slope which increases with grid-cell width.
  5. Additional microphysical processes, including ice nucleation and cloud ice sedimentation, were introduced.
In the Split GFDL Microphysics first implemented within SHiELD, microphysical processes were divided into fast and (relatively) slow processes, where the fast processes (primarily phase changes and latent heating/cooling) are updated after the vertical remapping in FV3, while the slower processes remain in the physical driver. More recently, the entire GFDL microphysics was Inlined within the dynamical core. The advantages of Inlining are 1) to separate the physical processes based on different time scales to better interact with dynamics processes; and 2) to be able to make the physical parameterization thermodynamically consistent with the dynamical core. Other updates in the Inline microphysics include a time-implicit monotonic scheme for sedimentation to ensure stability without needing to subcycle; precise conservation of the total moist energy; and transportation of heat and momentum carried by condensates during sedimentation.
Appendix C: A Note on Terminology
The term “model” means many different things in many contexts, and can be confusing. In this paper, we use the term “model” only in the abstract (“other general-purpose models”, “NCEP Modeling Suite”) or as part of the name of another system (“Noah Land Surface Model”, “GFDL Hurricane Model”). For concreteness, we refer to SHiELD as a “modeling system” which can be used in a variety of “configurations” (13-km SHiELD, C-SHiELD, T-SHiELD, S-SHiELD), each upgraded to new yearly versions (SHiELD 2016, SHiELD 2017, etc.).
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