Lucas Harris

Physical Scientist

Deputy Division Leader, Weather and Climate Dynamics Division

NOAA/Geophysical Fluid Dynamics Laboratory

Email: Lucas.Harris@noaa.gov

My research is focused on the development of the algorithms and software within the GFDL Finite-Volume Cubed-Sphere Dynamical Core, FV3, and its applications in the comprehensive weather and climate models fvGFS, HiRAM, and the next-generation AM4.

My personal expertise is on grid refinement techniques. The two methods for doing this in FV3 are grid nesting and grid stretching. These techniques allow FV3-powered models to be run at a very high resolution over a limited area convection-resolving forecasting, seasonal prediction, and regional climate modeling. Here is an introduction to variable-resolution techniques. Currently our group is using grid nesting and grid stretching to develop global models suitable for storm-scale severe thunderstorm and hurricane forecasting, and for subseasonal prediction of intense hurricanes.

Recent presentations:

• I have given a semi-technical introduction for non-specialists, entitled “FV3: The Present and Future of Weather and Climate Modeling”, most recently for the 2017 NOAA Science Days. The slides can be seen here, and the recording of the public media briefing is also available (my segment starts at about 20:40).
• A brief technical introduction to FV3 was given for DCMIP 2016.
• A longer technical presentation of the solver and of grid refinement in FV3 have been given, most recently in June 2018.
• In May 2017, GFDL was represented for the first time at the Hazardous Weather Testbed’s Spring Forecasting Experiment. Five-day forecasts from our global-to-3-km nested fvGFS were submitted to HWT for evaluation, which is forthcoming. A presentation summarizing our own analysis of the results was given as an NGGPS virtual seminar. Results from later experiments are being processed.

Other projects and documents

I have written a simple but efficient and highly flexible feature tracker, primarily for tropical and extratropical cyclones. Email me if you would like further information.

I have a few nice GrADS scripts, along with examples, that I use for some of my work that others may find helpful.

Ray Pierrehumbert’s classic essay on mountain gravity-wave drag parameterization is difficult to find online. A copy is available at ECMWF. (Many other excellent ECMWF conference proceedings, including many classic contributions by GFDL scientists, are available as well.) A conference proceeding describing the use of the Pierrehumbert and Wyman scheme in the Miyakoda GFDL model, also hard to find, is available here.

My colleague Xi Chen and I have submitted a comment on an article about grid staggering.

Publications

1. Delworth, Thomas L., William F Cooke, Alistair Adcroft, Mitchell Bushuk, Jan-Huey Chen, Krista A Dunne, Paul Ginoux, Richard G Gudgel, Robert Hallberg, Lucas Harris, Matthew J Harrison, Nathaniel C Johnson, Sarah B Kapnick, Shian-Jiann Lin, Feiyu Lu, Sergey Malyshev, P C D Milly, Hiroyuki Murakami, Vaishali Naik, S Pascale, David J Paynter, Anthony Rosati, M Daniel Schwarzkopf, Elena Shevliakova, Seth D Underwood, Andrew T Wittenberg, Baoqiang Xiang, Xiaosong Yang, Fanrong Zeng, Honghai Zhang, Liping Zhang, and Ming Zhao, March 2020: SPEAR – the next generation GFDL modeling system for seasonal to multidecadal prediction and projection. Journal of Advances in Modeling Earth Systems, 12(3), doi:10.1029/2019MS001895.
   [ Abstract ]

   We document the development and simulation characteristics of the next generation modeling system for seasonal to decadal prediction and projection at the Geophysical Fluid Dynamics Laboratory (GFDL). SPEAR (Seamless System for Prediction and EArth System Research) is built from component models recently developed at GFDL ‐ the AM4 atmosphere model, MOM6 ocean code, LM4 land model and SIS2 sea ice model. The SPEAR models are specifically designed with attributes needed for a prediction model for seasonal to decadal time scales, including the ability to run large ensembles of simulations with available computational resources. For computational speed SPEAR uses a coarse ocean resolution of approximately 1.0o (with tropical refinement). SPEAR can use differing atmospheric horizontal resolutions ranging from 1o to 0.25o. The higher atmospheric resolution facilitates improved simulation of regional climate and extremes. SPEAR is built from the same components as the GFDL CM4 and ESM 4 models, but with design choices geared toward seasonal to multidecadal physical climate prediction and projection. We document simulation characteristics for the time‐mean climate, aspects of internal variability, and the response to both idealized and realistic radiative forcing change. We describe in greater detail one focus of the model development process that was motivated by the importance of the Southern Ocean to the global climate system. We present sensitivity tests that document the influence of the Antarctic surface heat budget on Southern Ocean ventilation and deep global ocean circulation. These findings were also useful in the development processes for the GFDL CM4 and ESM 4 models.

2. Harris, Lucas, Linjiong Zhou, Xi Chen, and Jan-Huey Chen, January 2020: The GFDL Finite-Volume Cubed-Sphere Dynamical Core: Release 201912, Princeton, NJ: GFDL Weather and Climate Dynamics Division Technical Memorandum GFDL2020001, doi:10.25923/7h88-c53410pp.
   [ Abstract ]

   This technical note explains updates to the GFDL Finite-Volume Cubed-Sphere Dynamical Core, abbreviated FV3 or FV[superscript 3], and the Split GFDL Microphysics. It does not repeat the contents of earlier documentation, especially publications. A list of publications and prior technical notes describing FV3 is available on the GFDL website.

3. Chen, Jan-Huey, Shian-Jiann Lin, L Magnusson, Morris A Bender, Xi Chen, Linjiong Zhou, Baoqiang Xiang, Shannon L Rees, Matthew J Morin, and Lucas Harris, April 2019: Advancements in Hurricane Prediction with NOAA's Next Generation Forecast System. Geophysical Research Letters, 46(8), doi:10.1029/2019GL082410.
   [ Abstract ]

   We use the fvGFS model developed at the Geophysical Fluid Dynamics Laboratory (GFDL) to demonstrate the potential of the upcoming United States Next Generation Global Prediction System for hurricane prediction. The fvGFS retrospective forecasts initialized with the European Centre for Medium‐Range Weather Forecasts (ECMWF) data showed much‐improved track forecasts for the 2017 Atlantic hurricane season compared to the best performing ECMWF operational model. The fvGFS greatly improved the ECMWF's poor track forecast for Hurricane Maria (2017). For Hurricane Irma (2017), a well‐predicted case by the ECMWF model, the fvGFS produced even lower 5‐day track forecast errors. The fvGFS also showed better intensity prediction than both the United States and the ECMWF operational models, indicating the robustness of its numerical algorithms.

4. Gao, Kun, Lucas Harris, Jan-Huey Chen, Shian-Jiann Lin, and Andrew T Hazelton, January 2019: Improving AGCM Hurricane Structure With Two‐Way Nesting. Journal of Advances in Modeling Earth Systems, 11(1), doi:10.1029/2018MS001359.
   [ Abstract ]

   We demonstrate that two‐way nesting significantly improves the structure of simulated hurricane in an atmospheric general circulation model. Two sets of 30‐day hindcast experiments are conducted, one with the global‐uniform‐resolution (approximately 25‐km nominal horizontal resolution) and the other with a regionally refined two‐way nest (approximately 8 km over the tropical North Atlantic). The increase in the horizontal resolution on the nested grid improves the representation of storm intensity and intensification rate. When normalized by the radius of maximum wind (RMW), composite hurricane structures are generally similar in both simulations and compare well to observations. However, the hurricanes in the globally uniform configuration have much larger RMWs than observed, while those in the two‐way‐nested configuration have more realistic RMWs. We also find that the representation of the RMW has a critical impact on the simulation of inertial stability and boundary‐layer convergence in the inner‐core region. The more realistic inner‐core size (indicated by RMW) and structure are possible reasons for the improved intensification rates in the two‐way‐nested configuration.

5. Gao, Kun, Jan-Huey Chen, Lucas Harris, Yongqiang Sun, and Shian-Jiann Lin, August 2019: Skillful Prediction of Monthly Major Hurricane Activity in the North Atlantic with Two‐way Nesting. Geophysical Research Letters, 46(15), doi:10.1029/2019GL083526.
   [ Abstract ]

   We investigate the monthly prediction of North Atlantic hurricane and especially major hurricane activity based on the Geophysical Fluid Dynamics Laboratory High‐Resolution Atmospheric Model (HiRAM). We compare the performance of two versions of HiRAM: a globally‐uniform 25‐km grid and the other with an 8‐km interactive nest over the tropical North Atlantic. Both grid configurations show skills in predicting anomalous monthly hurricane frequency and accumulated cyclone energy (ACE). Particularly the 8‐km nested model shows improved skills in predicting major hurricane frequency and ACE. The skill in anomalous monthly hurricane occurrence prediction arises from the accurate prediction of zonal wind shear anomalies in the Main Development Region, which in turn arises from the SST anomalies persisted from the initialization time. The enhanced resolution on the nested grid permits a better representation of hurricanes and especially intense hurricanes, thereby showing the ability and the potential for prediction of major hurricanes on subseasonal timescales.

6. Harris, Lucas, Shannon L Rees, Matthew J Morin, Linjiong Zhou, and William F Stern, June 2019: Explicit prediction of continental convection in a skillful variable‐resolution global model. Journal of Advances in Modeling Earth Systems, 11(6), doi:10.1029/2018MS001542.
   [ Abstract ]

   We present a new global‐to‐regional model, cfvGFS, able to explicitly (without parameterization) represent convection over part of the earth. This model couples the Geophysical Fluid Dynamics Laboratory Finite‐Volume Cubed‐Sphere Dynamical Core (FV3) to the Global Forecast System (GFS) physics and initial conditions, augmented with a six‐category microphysics and a modified planetary boundary layer scheme. We examine the characteristics of cfvGFS on a 3‐km continental United States domain nested within a 13‐km global model. The nested cfvGFS still has good hemispheric skill comparable to or better than the operational GFS, while supercell thunderstorms, squall lines, and derechos are explicitly‐represented over the refined region. In particular, cfvGFS has excellent representations of fine‐scale updraft helicity fields, an important proxy for severe weather forecasting. Precipitation biases are found to be smaller than in uniform‐resolution global models and competitive with operational regional models; the 3‐km domain also improves upon the global models in 2‐m temperature and humidity skill. We discuss further development of cfvGFS and the prospects for a unified global‐to‐regional prediction system.

7. Held, Isaac M., Huan Guo, Alistair Adcroft, John P Dunne, Larry W Horowitz, John P Krasting, Elena Shevliakova, Michael Winton, Ming Zhao, Mitchell Bushuk, Andrew T Wittenberg, Bruce Wyman, Baoqiang Xiang, Rong Zhang, Whit G Anderson, V Balaji, Leo J Donner, Krista A Dunne, J W Durachta, Paul P G Gauthier, Paul Ginoux, Jean-Christophe Golaz, Stephen M Griffies, Robert Hallberg, Lucas Harris, Matthew J Harrison, William J Hurlin, Jasmin G John, Pu Lin, Shian-Jiann Lin, Sergey Malyshev, Raymond Menzel, P C D Milly, Yi Ming, Vaishali Naik, David J Paynter, Fabien Paulot, V Ramaswamy, Brandon G Reichl, Thomas E Robinson, Anthony Rosati, Charles J Seman, Levi G Silvers, Seth D Underwood, and Niki Zadeh, November 2019: Structure and Performance of GFDL's CM4.0 Climate Model. Journal of Advances in Modeling Earth Systems, 11(11), doi:10.1029/2019MS001829.
   [ Abstract ]

   We describe GFDL's CM4.0 physical climate model, with emphasis on those aspects that may be of particular importance to users of this model and its simulations. The model is built with the AM4.0/LM4.0 atmosphere/land model and OM4.0 ocean model. Topics include the rationale for key choices made in the model formulation, the stability as well as drift of the pre‐industrial control simulation, and comparison of key aspects of the historical simulations with observations from recent decades. Notable achievements include the relatively small biases in seasonal spatial patterns of top‐of‐atmosphere fluxes, surface temperature, and precipitation; reduced double Intertropical Convergence Zone bias; dramatically improved representation of ocean boundary currents; a high quality simulation of climatological Arctic sea ice extent and its recent decline; and excellent simulation of the El Niño‐Southern Oscillation spectrum and structure. Areas of concern include inadequate deep convection in the Nordic Seas; an inaccurate Antarctic sea ice simulation; precipitation and wind composites still affected by the equatorial cold tongue bias; muted variability in the Atlantic Meridional Overturning Circulation; strong 100 year quasi‐periodicity in Southern Ocean ventilation; and a lack of historical warming before 1990 and too rapid warming thereafter due to high climate sensitivity and strong aerosol forcing, in contrast to the observational record. Overall, CM4.0 scores very well in its fidelity against observations compared to the Coupled Model Intercomparison Project Phase 5 generation in terms of both mean state and modes of variability and should prove a valuable new addition for analysis across a broad array of applications.

8. Potvin, C K., J R Carley, A Clark, L J Wicker, P S Skinner, A E Reinhart, B T Gallo, J S Kain, G Romine, E Aligo, K Brewster, D C Dowell, and Lucas Harris, et al., October 2019: Systematic comparison of convection-allowing models during the 2017 NOAA HWT Spring Forecasting Experiment. Weather and Forecasting, 34(5), doi:10.1175/WAF-D-19-0056.1.
   [ Abstract ]

   The 2016–2018 NOAA Hazardous Weather Testbed (HWT) Spring Forecasting Experiments (SFE) featured the Community Leveraged Unified Ensemble (CLUE), a coordinated convection-allowing model (CAM) ensemble framework designed to provide empirical guidance for development of operational CAM systems. The 2017 CLUE included 81 members that all used 3-km horizontal grid spacing over the CONUS, enabling direct comparison of forecasts generated using different dynamical cores, physics schemes, and initialization procedures. This study uses forecasts from several of the 2017 CLUE members and one operational model to evaluate and compare CAM representation and next-day prediction of thunderstorms. The analysis utilizes existing techniques and novel, object-based techniques that distill important information about modeled and observed storms from many cases. The National Severe Storms Laboratory Multi-Radar/Multi-Sensor product suite is used to verify model forecasts and climatologies of observed variables. Unobserved model fields are also examined to further illuminate important inter-model differences in storms and near-storm environments. No single model performed better than the others in all respects. However, there were many systematic inter-model and inter-core differences in specific forecast metrics and model fields. Some of these differences can be confidently attributed to particular differences in model design. Model intercomparison studies similar to the one presented here are important to better understand the impacts of model and ensemble configurations on storm forecasts and to help optimize future operational CAM systems.

9. Vecchi, Gabriel A., Thomas L Delworth, Hiroyuki Murakami, Seth D Underwood, Andrew T Wittenberg, Fanrong Zeng, Wei Zhang, Jane Baldwin, Kieran Bhatia, William F Cooke, Jie He, Sarah B Kapnick, Thomas R Knutson, G Villarini, Karin van der Wiel, Whit G Anderson, V Balaji, Jan-Huey Chen, Keith W Dixon, Richard G Gudgel, Lucas Harris, Liwei Jia, Nathaniel C Johnson, Shian-Jiann Lin, Maofeng Liu, Chin Ho Justin Ng, Anthony Rosati, J A Smith, and Xiaosong Yang, November 2019: Tropical cyclone sensitivities to CO2 doubling: roles of atmospheric resolution, synoptic variability and background climate changes. Climate Dynamics, 53(9-10), doi:10.1007/s00382-019-04913-y.
   [ Abstract ]

   Responses of tropical cyclones (TCs) to CO2 doubling are explored using coupled global climate models (GCMs) with increasingly refined atmospheric/land horizontal grids (~ 200 km, ~ 50 km and ~ 25 km). The three models exhibit similar changes in background climate fields thought to regulate TC activity, such as relative sea surface temperature (SST), potential intensity, and wind shear. However, global TC frequency decreases substantially in the 50 km model, while the 25 km model shows no significant change. The ~ 25 km model also has a substantial and spatially-ubiquitous increase of Category 3–4–5 hurricanes. Idealized perturbation experiments are performed to understand the TC response. Each model’s transient fully-coupled 2 × CO2 TC activity response is largely recovered by “time-slice” experiments using time-invariant SST perturbations added to each model’s own SST climatology. The TC response to SST forcing depends on each model’s background climatological SST biases: removing these biases leads to a global TC intensity increase in the ~ 50 km model, and a global TC frequency increase in the ~ 25 km model, in response to CO2-induced warming patterns and CO2 doubling. Isolated CO2 doubling leads to a significant TC frequency decrease, while isolated uniform SST warming leads to a significant global TC frequency increase; the ~ 25 km model has a greater tendency for frequency increase. Global TC frequency responds to both (1) changes in TC “seeds”, which increase due to warming (more so in the ~ 25 km model) and decrease due to higher CO2 concentrations, and (2) less efficient development of these“seeds” into TCs, largely due to the nonlinear relation between temperature and saturation specific humidity.

10. Zarzycki, C M., C Jablonowski, J Kent, P H Lauritzen, R Nair, Kevin A Reed, P A Ullrich, D M Hall, D Dazlich, R Heikes, C Konor, David A Randall, Xi Chen, and Lucas Harris, et al., March 2019: DCMIP2016: the splitting supercell test case. Geoscientific Model Development, 12(3), doi:10.5194/gmd-12-879-2019.
    [ Abstract ]

    This paper describes the splitting supercell idealized test case used in the 2016 Dynamical Core Model Intercomparison Project (DCMIP2016). These storms are useful testbeds for global atmospheric models because the horizontal scale of convective plumes is O(1km), emphasizing non-hydrostatic dynamics. The test case simulates a supercell on a reduced radius sphere with nominal resolutions ranging from 4km to 0.5km and is based on the work of Klemp et al. (2015). Models are initialized with an atmospheric environment conducive to supercell formation and forced with a small thermal perturbation. A simplified Kessler microphysics scheme is coupled to the dynamical core to represent moist processes. Reference solutions for DCMIP2016 models are presented. Storm evolution is broadly similar between models, although differences in final solution exist. These differences are hypothesized to result from different numerical discretizations, physics-dynamics coupling, and numerical diffusion. Intramodel solutions generally converge as models approach 0.5km resolution. These results can be used as a reference for future dynamical core evaluation, particularly with the development of non-hydrostatic global models intended to be used in convective-permitting and convective-allowing regimes.

11. Zhang, F, M Minamide, R G Nystrom, X Chen, Shian-Jiann Lin, and Lucas Harris, July 2019: Improving Harvey forecasts with next-generation weather satellites. Bulletin of the American Meteorological Society, 100(7), doi:10.1175/BAMS-D-18-0149.1.
    [ Abstract ]

    The experimental forecasts initialized with the ensemble assimilation of the all-sky radiances—from the next-generation satellite (GOES-16)—has demonstrated its potential in more accurate prediction of Hurricane Harvey (2017) before its rapid intensification. Hurricane Harvey brought catastrophic destruction and historical flooding to the Gulf Coast region in late August 2017. Guided by numerical weather prediction models, operational forecasters at NOAA provided outstanding forecasts of Harvey’s future path and potential for record flooding days in advance. These forecasts were valuable to the public and emergency managers in protecting lives and property. The current study shows the potential for further improving Harvey’s analysis and prediction through advanced ensemble assimilation of high-spatiotemporal all-sky infrared radiances from the newly-launched, next-generation geostationary weather satellite, GOES-16. Although findings from this single-event study should be further evaluated, the results highlight the potential improvement in hurricane prediction that is possible via sustained investment in advanced observing systems, such as those from weather satellites, comprehensive data assimilation methodologies that can more effectively ingest existing and future observations, higher-resolution weather prediction models with more accurate numerics and physics, and high-performance computing facilities that can perform advanced analysis and forecasting in a timely manner.

12. Zhang, C, M Xue, T A Supinie, F Kong, N Snook, K W Thomas, K Brewster, Y Jung, Lucas Harris, and Shian-Jiann Lin, March 2019: How Well Does an FV3-based Model Predict Precipitation at a Convection-Allowing Resolution? Results from CAPS Forecasts for the 2018 NOAA Hazardous Weather Testbed with Different Physics Combinations. Geophysical Research Letters, 46(6), doi:10.1029/2018GL081702.
    [ Abstract ]

    The Geophysical Fluid Dynamics Laboratory (GFDL) Finite‐Volume Cubed‐Sphere (FV3) numerical forecast model was chosen in late 2016 by the National Weather Service (NWS) to serve as the dynamic core of the Next‐Generation Global Prediction System (NGGPS). The operational Global Forecasting System (GFS) physics suite implemented in FV3, however, was not necessarily suitable for convective‐scale prediction. We implemented several advanced physics schemes from the Weather Research and Forecasting (WRF) model within FV3 and ran 10 forecasts with combinations of five planetary boundary layer and two microphysics (MP) schemes, with an ~3.5‐km convection‐allowing grid two‐way nested within am ~13‐km grid spacing global grid during the 2018 Spring Forecasting Experiment at National Oceanic and Atmospheric Administration (NOAA)'s Hazardous Weather Testbed. Objective verification results show that the Thompson MP scheme slightly outperforms the National Severe Storms Laboratory MP scheme in precipitation forecast skill, while no planetary boundary layer scheme clearly stands out. The skill of FV3 is similar to that of the more‐established WRF at a similar resolution. These results establish the viability of the FV3 dynamic core for convective‐scale forecasting as part of the single‐core unification of the NWS modeling suite.

13. Zhou, Linjiong, Shian-Jiann Lin, Jan-Huey Chen, Lucas Harris, Xi Chen, and Shannon L Rees, July 2019: Toward Convective-Scale Prediction within the Next Generation Global Prediction System. Bulletin of the American Meteorological Society, 100(7), doi:10.1175/BAMS-D-17-0246.1.
    [ Abstract ]

    The variable-resolution version of a Finite-Volume Cubed-Sphere Dynamical Core (FV3)-based global model improves the prediction of convective-scale features while maintaining skillful global forecasts. The Geophysical Fluid Dynamics Laboratory (GFDL) has developed a new variable-resolution global model with the ability to represent convective-scale features that serves as a prototype of the Next Generation Global Prediction System (NGGPS). The goal of this prediction system is to maintain the skill in large-scale features while simultaneously improving the prediction skill of convectively-driven mesoscale phenomena. This paper demonstrates the new capability of this model in convective-scale prediction relative to the current operational Global Forecast System (GFS). This model uses the stretched-grid functionality of the Finite-Volume Cubed-Sphere Dynamical Core (FV3) to refine the global 13-km uniform-resolution model down to 4-km convection-permitting resolution over the Contiguous United States (CONUS), and implements the GFDL single-moment six-category cloud microphysics to improve the representation of moist processes. Statistics gathered from two years of simulations by the GFS and select configurations of the FV3-based model are carefully examined. The variable-resolution FV3-based model is shown to possess global forecast skill comparable with that of the operational GFS while quantitatively improving skill and better representing the diurnal cycle within the high-resolution area compared to the uniform mesh simulations. Forecasts of the occurrence of extreme precipitation rates over the Southern Great Plains are also shown to improve with the variable-resolution model. Case studies are provided of a squall line and a hurricane to demonstrate the effectiveness of the variable-resolution model to simulate convective-scale phenomena.

14. Anber, Usama, Nadir Jeevanjee, Lucas Harris, and Isaac M Held, July 2018: Sensitivity of Radiative‐Convection Equilibrium to Divergence Damping in GFDL‐FV3 Based Cloud‐Resolving Model Simulations. Journal of Advances in Modeling Earth Systems, 10(7), doi:10.1029/2017MS001225.
    [ Abstract ]

    Using a non‐hydrostatic model based on a version of GFDL's FV3 dynamical core at a cloud‐resolving resolution in radiative‐convective equilibrium (RCE) configuration, the sensitivity of the mean RCE climate to the magnitude and scale‐selectivity of the divergence damping is explored. Divergence damping is used to reduce small‐scale noise in more realistic configurations of this model. This sensitivity is tied to the strength (and width) of the convective updrafts, which decreases (increases) with increased damping and acts to organize the convection, dramatically drying out the troposphere and increasing the outgoing longwave radiation. Increased damping also results in a much‐broadened precipitation probability distribution and larger extreme values, as well as reduction in cloud fraction, which correspondingly decreases the magnitude of shortwave and longwave cloud radiative effects. Solutions exhibit a monotonic dependence on the strength of the damping and asymptotically converge to the inviscid limit. While the potential dependence of RCE simulations on resolution and microphysical assumptions are generally appreciated, these results highlight the potential significance of the choice of sub‐grid numerical diffusion in the dynamical core.

15. Chen, Xi, Shian-Jiann Lin, and Lucas Harris, September 2018: Towards an unstaggered finite‐volume dynamical core with a fast Riemann solver: 1D linearized analysis of dissipation, dispersion, and noise control. Journal of Advances in Modeling Earth Systems, 10(9), doi:10.1029/2018MS001361.
    [ Abstract ]

    Many computational fluid dynamics codes use Riemann solvers on an unstaggered grid for finite volume methods, but this approach is computationally expensive compared to existing atmospheric dynamical cores equipped with hyper‐diffusion or other similar relatively simple diffusion forms. We present a simplified Low Mach number Approximate Riemann Solver (LMARS), made computationally efficient through assumptions appropriate for atmospheric flows: low Mach number, weak discontinuities, and locally‐uniform sound speed. This work will examine the dissipative and dispersive properties of LMARS using Von Neumann linearized analysis to the one‐dimensional linearized shallow water equations. We extend these analyses to higher‐order methods by numerically solving the Fourier‐transformed equations. It is found that the pros and cons due to grid staggering choices diminish with high‐order schemes. The linearized analysis is limited to modal, smooth solutions using simple numerical schemes, and cannot analyze solutions with discontinuities. To address this problem, this work presents a new idealized test of a discontinuous wave packet, a single Fourier mode modulated by a discontinuous square‐wave. The experiments include studies of well‐resolved and (near) grid‐scale wave profiles, as well as the representation of discontinuous features and the results are validated against the Von Neumann analysis. We find the higher‐order LMARS produces much less numerical noise than do inviscid unstaggered and especially staggered schemes while retaining accuracy for better‐resolved modes.

16. Hazelton, Andrew T., Lucas Harris, and Shian-Jiann Lin, April 2018: Evaluation of Tropical Cyclone Structure Forecasts in a High-Resolution Version of the Multiscale GFDL fvGFS Model. Weather and Forecasting, 33(2), doi:10.1175/WAF-D-17-0140.1.
    [ Abstract ]

    A nested version of the FV3 dynamical core with GFS physics (fvGFS) is capable of tropical cyclone (TC) prediction across multiple space and time scales, from subseasonal prediction to high-resolution structure and intensity forecasting. Here, a version of fvGFS with 2 km resolution covering most of the North Atlantic is evaluated for its ability to simulate TC track, intensity, and fine-scale structure. TC structure is evaluated through comparison of forecasts with 3-dimensional Doppler radar from P-3 flights by NOAA’s Hurricane Research Division (HRD), and structural metrics evaluated include the 2-km radius of maximum wind (RMW), slope of the RMW, depth of the TC vortex, and horizontal vortex decay rate. 7 TCs from the 2010-2016 seasons are evaluated, including 10 separate model runs and 38 individual flights. The model had some success in producing rapid intensification (RI) forecasts for Earl, Edouard, and Matthew. fvGFS successfully predicts RMW in the 25-50 km range, but tends to have a small bias at very large radii and a large bias at very small radii. The wind peak also tends to be somewhat too sharp, and the vortex depth occasionally has a high bias, especially for storms that are observed to be shallow. Composite radial wind shows that the boundary layer tends to be too deep, although the outflow structure aloft is relatively consistent with observations. These results highlight the utility of structural evaluation of TC forecasts, and also show the promise of fvGFS for forecasting TCs.

17. Hazelton, Andrew T., Morris A Bender, Matthew J Morin, Lucas Harris, and Shian-Jiann Lin, October 2018: 2017 Atlantic Hurricane Forecasts From a High-Resolution Version of the GFDL fvGFS Model: Evaluation of Track, Intensity, and Structure. Weather and Forecasting, 33(5), doi:10.1175/WAF-D-18-0056.1.
    [ Abstract ]

    The 2017 Atlantic hurricane season had several high-impact tropical cyclones (TCs), including multiple cases of rapid intensification (RI). A high-resolution nested version of the GFDL fvGFS model (HifvGFS) was used to conduct hindcasts of all Atlantic TCs between August 7 and October 15. HifvGFS showed promising track forecast performance, with similar error patterns and skill compared to the operational GFS and HWRF models. Some of the larger track forecast errors were associated with the erratic tracks of Jose and Lee. A case study of Maria found that although the track forecasts were generally skillful, a right-of-track bias was noted in some cases associated with initialization and prediction of ridging north of the storm. The intensity forecasts showed large improvement over the GFS and global fvGFS models, but were somewhat less skillful than HWRF. The largest negative intensity forecast errors were associated with the RI of Irma, Lee, and Maria, while the largest positive errors were found with recurving cases that were generally weakening. The structure forecasts were also compared with observations, and HifvGFS was found to generally have wind radii larger than observations. Detailed examination of the forecasts of Hurricanes Harvey and Maria showed that HifvGFS was able to predict the structural evolution leading to RI in some cases, but was not as skillful with other RI cases. One case study of Maria suggested that inclusion of ocean coupling could significantly reduce the positive bias seen during and after recurvature.

18. Zhao, Ming, Jean-Christophe Golaz, Isaac M Held, Huan Guo, V Balaji, Rusty Benson, Jan-Huey Chen, Xi Chen, Leo J Donner, John P Dunne, Krista A Dunne, J W Durachta, Songmiao Fan, Stuart Freidenreich, Stephen T Garner, Paul Ginoux, Lucas Harris, Larry W Horowitz, John P Krasting, Amy R Langenhorst, Zhi Liang, Pu Lin, Shian-Jiann Lin, Sergey Malyshev, E Mason, P C D Milly, Yi Ming, Vaishali Naik, Fabien Paulot, David J Paynter, Peter Phillipps, Aparna Radhakrishnan, V Ramaswamy, Thomas E Robinson, M Daniel Schwarzkopf, Charles J Seman, Elena Shevliakova, Zhaoyi Shen, Hyeyum Hailey Shin, Levi G Silvers, R John Wilson, Michael Winton, Andrew T Wittenberg, Bruce Wyman, and Baoqiang Xiang, March 2018: The GFDL Global Atmosphere and Land Model AM4.0/LM4.0 - Part I: Simulation Characteristics with Prescribed SSTs. Journal of Advances in Modeling Earth Systems, 10(3), doi:10.1002/2017MS001208.
    [ Abstract ]

    In this two-part paper, a description is provided of a version of the AM4.0/LM4.0 atmosphere/land model that will serve as a base for a new set of climate and Earth system models (CM4 and ESM4) under development at NOAA's Geophysical Fluid Dynamics Laboratory (GFDL). This version, with roughly 100km horizontal resolution and 33 levels in the vertical, contains an aerosol model that generates aerosol fields from emissions and a “light” chemistry mechanism designed to support the aerosol model but with prescribed ozone. In Part I, the quality of the simulation in AMIP (Atmospheric Model Intercomparison Project) mode – with prescribed sea surface temperatures (SSTs) and sea ice distribution – is described and compared with previous GFDL models and with the CMIP5 archive of AMIP simulations. The model's Cess sensitivity (response in the top-of-atmosphere radiative flux to uniform warming of SSTs) and effective radiative forcing are also presented. In Part II, the model formulation is described more fully and key sensitivities to aspects of the model formulation are discussed, along with the approach to model tuning.

19. Zhao, Ming, Jean-Christophe Golaz, Isaac M Held, Huan Guo, V Balaji, Rusty Benson, Jan-Huey Chen, Xi Chen, Leo J Donner, John P Dunne, Krista A Dunne, J W Durachta, Songmiao Fan, Stuart Freidenreich, Stephen T Garner, Paul Ginoux, Lucas Harris, Larry W Horowitz, John P Krasting, Amy R Langenhorst, Zhi Liang, Pu Lin, Shian-Jiann Lin, Sergey Malyshev, E Mason, P C D Milly, Yi Ming, Vaishali Naik, Fabien Paulot, David J Paynter, Peter Phillipps, Aparna Radhakrishnan, V Ramaswamy, Thomas E Robinson, M Daniel Schwarzkopf, Charles J Seman, Elena Shevliakova, Zhaoyi Shen, Hyeyum Hailey Shin, Levi G Silvers, R John Wilson, Michael Winton, Andrew T Wittenberg, Bruce Wyman, and Baoqiang Xiang, March 2018: The GFDL Global Atmosphere and Land Model AM4.0/LM4.0 - Part II: Model Description, Sensitivity Studies, and Tuning Strategies. Journal of Advances in Modeling Earth Systems, 10(3), doi:10.1002/2017MS001209.
    [ Abstract ]

    In Part II of this two-part paper, documentation is provided of key aspects of a version of the AM4.0/LM4.0 atmosphere/land model that will serve as a base for a new set of climate and Earth system models (CM4 and ESM4) under development at NOAA's Geophysical Fluid Dynamics Laboratory (GFDL). The quality of the simulation in AMIP (Atmospheric Model Intercomparison Project) mode has been provided in Part I. Part II provides documentation of key components and some sensitivities to choices of model formulation and values of parameters, highlighting the convection parameterization and orographic gravity wave drag. The approach taken to tune the model's clouds to observations is a particular focal point. Care is taken to describe the extent to which aerosol effective forcing and Cess sensitivity have been tuned through the model development process, both of which are relevant to the ability of the model to simulate the evolution of temperatures over the last century when coupled to an ocean model.

20. Gao, Kun, Jan-Huey Chen, Lucas Harris, Shian-Jiann Lin, Baoqiang Xiang, and Ming Zhao, December 2017: Impact of Intraseasonal Oscillations on the Tropical Cyclone Activity over the Gulf of Mexico and Western Caribbean Sea in GFDL HiRAM. Journal of Geophysical Research: Atmospheres, 122(24), doi:10.1002/2017JD027756.
    [ Abstract ]

    The Tropical Cyclones (TC) that form over the warm waters in the Gulf of Mexico region pose a major threat to the surrounding coastal communities. Skillful sub-seasonal prediction of TC activity is important for early preparedness and reducing the TC damage in this region. In this study, we evaluate the performance of a 25-km resolution Geophysical Fluid Dynamics Laboratory (GFDL) High Resolution Atmospheric Model (HiRAM) in simulating the modulation of the TC activity in the Gulf of Mexico and western Caribbean Sea by the Intraseasonal Oscillation (ISO) based on multi-year retrospective seasonal predictions. We demonstrate that the HiRAM faithfully captures the observed influence of ISO on TC activity over the region of interest, including the formation of tropical storms and (major) hurricanes, as well as the landfalling storms. This is likely because of the realistic representation of the large-scale anomalies associated with boreal summer ISO over Northeast Pacific in HiRAM, especially the enhanced (reduced) moisture throughout the troposphere during the convectively enhanced (suppressed) phase of ISO. The reasonable performance of HiRAM suggests its potential for the subseasonal prediction of regional TC risk.

21. Lin, Shian-Jiann, Lucas Harris, Xi Chen, Weiye Yao, and Junyi Chai, November 2017: Colliding Modons: A Nonlinear Test for the Evaluation of Global Dynamical Cores. Journal of Advances in Modeling Earth Systems, 9(7), doi:10.1002/2017MS000965.
    [ Abstract ]

    The modon, a pair of counter-rotating vortices propelling one another along a straight line, is an idealization of some observed large- and small-scale atmospheric and oceanic processes (e.g., twin cyclones), providing a challenging nonlinear test for fluid-dynamics solvers (known as “dynamical cores”). We present an easy-to-setup test of colliding modons suitable for both shallow-water and three-dimensional dynamical cores on the sphere. Two pairs of idealized modons are configured to collide, exchange vortices, and depart in opposite directions, repeating indefinitely in the absence of ambient rotation. This test is applicable to both hydrostatic and nonhydrostatic dynamical cores and particularly challenging for refined grids on the sphere, regardless of solution methodology or vertical coordinate. We applied this test to three popular dynamical cores, used by three different general circulation models: the spectral element core of the Community Atmosphere Model, the Geophysical Fluid Dynamics Laboratory (GFDL) spectral core, and the GFDL finite-volume cubed-sphere core, FV3. Tests with a locally-refined grid and nonhydrostatic dynamics were also performed with FV3. All cores tested were able to capture the propagation, collision, and exchange of the modons, albeit the rate at which the modon was diffused varied between the three cores and showed a strong dependence on the strength of hyper-diffusion.

22. Ullrich, P A., C Jablonowski, J Kent, P H Lauritzen, R Nair, Kevin A Reed, C M Zarzycki, D M Hall, D Dazlich, R Heikes, C Konor, David A Randall, T Dubos, Y Meurdesoif, Xi Chen, and Lucas Harris, et al., December 2017: DCMIP2016: a review of non-hydrostatic dynamical core design and intercomparison of participating models. Geoscientific Model Development, 10(12), doi:10.5194/gmd-10-4477-2017.
    [ Abstract ]

    Atmospheric dynamical cores are a fundamental component of global atmospheric modeling systems and are responsible for capturing the dynamical behavior of the Earth's atmosphere via numerical integration of the Navier–Stokes equations. These systems have existed in one form or another for over half of a century, with the earliest discretizations having now evolved into a complex ecosystem of algorithms and computational strategies. In essence, no two dynamical cores are alike, and their individual successes suggest that no perfect model exists. To better understand modern dynamical cores, this paper aims to provide a comprehensive review of 11 non-hydrostatic dynamical cores, drawn from modeling centers and groups that participated in the 2016 Dynamical Core Model Intercomparison Project (DCMIP) workshop and summer school. This review includes a choice of model grid, variable placement, vertical coordinate, prognostic equations, temporal discretization, and the diffusion, stabilization, filters, and fixers employed by each system.

23. Harris, Lucas, Shian-Jiann Lin, and C Tu, June 2016: High resolution climate simulations using GFDL HiRAM with a stretched global grid. Journal of Climate, 29(11), doi:10.1175/JCLI-D-15-0389.1.
    [ Abstract ]

    An analytic Schmidt transformation is used to create locally-refined global model grids capable of efficient climate simulation with grid-cell-widths as small as 10 km in the GFDL HIRAM model. This method of grid stretching produces a grid which varies very gradually into the region of enhanced resolution without changing the topology of the model grid and does not require radical changes to the solver. AMIP integrations were carried out with two grids stretched to 10 km minimum grid-cell width: one centered over east Asia and the western Pacific warm pool, and the other over the continental United States. Robust improvements to orographic precipitation, the diurnal cycle of warm-season continental precipitation, and tropical cyclone maximum intensity were found in the region of enhanced resolution, compared to 25-km uniform-resolution HiRAM. The variations in grid size were not found to create apparent grid artifacts, and in some measures the global-mean climate improved in the stretched-grid simulations. In the enhanced-resolution regions, the number of tropical cyclones was reduced, but the fraction of storms reaching hurricane intensity increased, compared to a uniform-resolution simulation. This behavior was also found in a stretched-grid perpetual-September aquaplanet simulation with 12-km resolution over a part of the tropics. Furthermore, the stretched-grid aquaplanet simulation was also largely free of grid artifacts except for an artificial Walker-type circulation, and simulated an ITCZ in its unrefined region more resembling that of higher-resolution Aquaplanet simulations, implying that the unrefined region may also be improved in stretched-grid simulations. The improvements due to stretching are attributable to improved resolution as these stretched-grid simulations were sparingly tuned.

24. Scott, R K., Lucas Harris, and L M Polvani, January 2016: A test case for the inviscid shallow water equations on the sphere. Quarterly Journal of the Royal Meteorological Society, 142(694), doi:10.1002/qj.2667.
    [ Abstract ]

    A numerically converged solution to the inviscid global shallow water equations on a predefined time interval is documented to provide a convenient benchmark for model validation. The solution is based on the same initial conditions as a previously documented solution for the viscous equations. The solution is computed using two independent numerical schemes, one a pseudospectral scheme based on an expansion in spherical harmonics, the other a finite-volume scheme on a cubed-sphere grid. Flow fields and various integral norms are both documented to facilitate model comparison and validation. Attention is drawn to the utility of the potential vorticity supremum as a convenient and sensitive test of numerical convergence, in which the exact value is known a priori over the entire time interval.

25. Zhang, Wei, Gabriel A Vecchi, Hiroyuki Murakami, Thomas L Delworth, Andrew T Wittenberg, Anthony Rosati, Seth D Underwood, Whit G Anderson, Lucas Harris, Richard G Gudgel, Shian-Jiann Lin, G Villarini, and Jan-Huey Chen, February 2016: Improved Simulation of Tropical Cyclone Responses to ENSO in the Western North Pacific in the High-Resolution GFDL HiFLOR Coupled Climate Model. Journal of Climate, 29(4), doi:10.1175/JCLI-D-15-0475.1.
    [ Abstract ]

    This study aims to assess whether, and the extent to which, an increase in atmospheric resolution in versions of the Geophysical Fluid Dynamics Laboratory (GFDL) High-Resolution Forecast-oriented Low Ocean Resolution Version of CM2.5 (FLOR) with 50 km and HiFLOR with 25 km improves the simulation of the El Niño Southern Oscillation-tropical cyclone (ENSO-TC) connections in the western North Pacific (WNP). HiFLOR simulates better ENSO-TC connections in the WNP including TC track density, genesis and landfall than FLOR in both long-term control experiments and sea surface temperature (SST)- and sea surface salinity (SSS)-restoring historical runs (1971-2012). Restoring experiments are performed with SSS and SST restored to observational estimates of climatological SSS and interannually-varying monthly SST. In the control experiments of HiFLOR, an improved simulation of the Walker circulation arising from more realistic SST and precipitation is largely responsible for its better performance in simulating ENSO-TC connections in the WNP. In the SST-restoring experiments of HiFLOR, more realistic Walker circulation and steering flow during El Niño/La Niña are responsible for the improved simulation of ENSO-TC connections in the WNP. The improved simulation of ENSO-TC connections with HiFLOR arises from a better representation of SST and better responses of environmental large-scale circulation to SST anomalies associated with El Niño/La Niña. A better representation of ENSO-TC connections in HiFLOR can benefit the seasonal forecasting of TC genesis, track and landfall, improve our understanding of the interannual variation of TC activity, and provide better projection of TC activity under climate change.

26. Fan, Songmiao, Lucas Harris, and Larry W Horowitz, November 2015: Atmospheric energy transport to the Arctic 1979-2012. Tellus A, 67, doi:10.3402/tellusa.v67.25482.
    [ Abstract ]

    The Arctic troposphere has warmed faster than the global average over the last several decades. It was suggested that atmospheric northward energy transport (ANET) into the Arctic had contributed to tropospheric warming in the Arctic. Here we calculate ANET based on the NCEP/NCAR reanalysis data from 1979 to 2012. During this period the zonally integrated energy flux into the Arctic has decreased rather than increased in all seasons. However, the trends are statistically insignificant except for the winter and annual mean fluxes. For the winter season, the transient eddy flux of energy increases over Greenland and the Greenland Sea and decreases over west-central Siberia (WCS). Trends in meridional wind variance and vorticity also indicate increasing transient eddy activity over Northern Canada, the Greenland Sea and the Norwegian Sea and decreasing activity over WCS. Inter-winter variations in local vorticity over the WCS are significantly anti-correlated with the Arctic climate.

27. Murakami, Hiroyuki, Gabriel A Vecchi, Seth D Underwood, Thomas L Delworth, Andrew T Wittenberg, Whit G Anderson, Jan-Huey Chen, Richard G Gudgel, Lucas Harris, Shian-Jiann Lin, and Fanrong Zeng, December 2015: Simulation and Prediction of Category 4 and 5 Hurricanes in the High-Resolution GFDL HiFLOR Coupled Climate Model. Journal of Climate, 28(23), doi:10.1175/JCLI-D-15-0216.1.
    [ Abstract ]

    A new high-resolution Geophysical Fluid Dynamics Laboratory (GFDL) coupled model (HiFLOR) has been developed and used to investigate potential skill in simulation and prediction of tropical cyclone (TC) activity. HiFLOR comprises of high-resolution (~25-km mesh) atmosphere and land components and a more moderate-resolution (~100-km mesh) sea ice and ocean components. HiFLOR was developed from the Forecast Oriented Low Resolution Ocean model (FLOR) by decreasing the horizontal grid spacing of the atmospheric component from 50-km to 25-km, while leaving most of the sub-gridscale physical parameterizations unchanged. Compared with FLOR, HiFLOR yields a more realistic simulation of the structure, global distribution, and seasonal and interannual variations of TCs, and a comparable simulation of storm-induced cold wakes and TC-genesis modulation induced by the Madden Julian Oscillation (MJO). Moreover, HiFLOR is able to simulate and predict extremely intense TCs (categories 4 and 5) and their interannual variations, which represents the first time a global coupled model has been able to simulate such extremely intense TCs in a multi-century simulation, sea surface temperature restoring simulations, and retrospective seasonal predictions.

28. Xiang, Baoqiang, Shian-Jiann Lin, Ming Zhao, Gabriel A Vecchi, T Li, X Jiang, Lucas Harris, and Jan-Huey Chen, February 2015: Beyond weather time scale prediction for Hurricane Sandy and Super Typhoon Haiyan in a global climate model. Monthly Weather Review, 143(2), doi:10.1175/MWR-D-14-00227.1.
    [ Abstract ]

    While tropical cyclone (TC) prediction, in particular TC genesis, remains very challenging, accurate prediction of TCs is critical for timely preparedness and mitigation. Using a new version of the Geophysical Fluid Dynamics Laboratory (GFDL) coupled model, the authors studied the predictability of two destructive landfall TCs, Hurricane Sandy in 2012 and Super Typhoon Haiyan in 2013. Results demonstrate that the geneses of these two TCs are highly predictable with the maximum prediction lead-time reaching 11 days. The “beyond weather time scale” predictability of tropical cyclogenesis is primarily attributed to the model’s skillful prediction of the intraseasonal Madden-Julian Oscillation (MJO) and the westward propagation of easterly waves. Meanwhile, the landfall location and time can be predicted one week ahead for Sandy’s U.S landfall, and two weeks ahead for Haiyan’s landing in the Philippines. The success in predicting Sandy and Haiyan, together with low false alarms, indicates the potential using the GFDL coupled model for operational extended-range predictions of TCs.

29. Harris, Lucas, and Shian-Jiann Lin, July 2014: Global-to-regional nested-grid climate simulations in the GFDL High Resolution Atmosphere Model. Journal of Climate, 27(13), doi:10.1175/JCLI-D-13-00596.1.
    [ Abstract ]

    A two-way nested-grid version of the Geophysical Fluid Dynamics Laboratory High Resolution Atmosphere Model (HiRAM) has been developed which uses simple methods for providing nested-grid boundary conditions and mass-conserving nested-to-global communication. Nested-grid simulations over the Maritime Continent and over North America were performed, each at two different resolutions: a 110-km mean grid-cell-width refined by a factor of three, and a 50-km mean grid-cell-width refined by a factor of two. Nested grid simulations were compared against uniform-resolution simulations, and against reanalyses, to determine the effect of grid nesting on both the modeled global climate and on the simulation of small-scale features. Orographically-forced precipitation was robustly found to be simulated with more detail and greater realism in a nested grid simulation compared with when only the coarse grids were simulated alone. Tropical precipitation biases were reduced in the Maritime continent region when a nested grid was introduced. Both results were robust to changes in the nested grid parameterization tunings. In North America, cold-season orographic precipitation was improved by nesting, but precipitation biases in the central and eastern United States were little changed. Improving the resolution through nesting also allowed for more intense rainfall events, greater Kelvin-wave activity, and stronger tropical cyclones. Nested grid boundary artifacts were more pronounced when a one-way, noninteractive nested grid was used.

30. Harris, Lucas, and Shian-Jiann Lin, January 2013: A two-way nested global-regional dynamical core on the cubed-sphere grid. Monthly Weather Review, 141(1), doi:10.1175/MWR-D-11-00201.1.
    [ Abstract ]

    A nested-grid model is constructed using the Geophysical Fluid Dynamics Laboratory Finite-Volume dynamical core on the cubed sphere. The use of a global grid avoids the need for externally-imposed lateral boundary conditions, and the use of the same governing equations and discretization on the global and regional domains prevents inconsistencies that may arise when these differ between grids. A simple interpolated nested-grid boundary condition is used, and two-way updates use a finite-volume averaging method. Mass conservation is achieved in two-way nesting by simply not updating the mass field. Despite the simplicity of the nesting methodology, the distortion of the large-scale flow by the nested grid is such that the increase in global error norms is a factor of two or less in shallow-water test cases. The effect of a nested grid in the tropics on the zonal means and eddy statistics of an idealized Held-Suarez climate integration is minor, and artifacts due to the nested grid are comparable to those at the edges of the cubed-sphere grid and decrease with increasing resolution. The baroclinic wave train in a Jablonowski-Williamson test case was preserved in a nested-grid simulation while fine-scale features were represented with greater detail in the nested-grid region. We also found that lee vortices could propagate out of the nested region and onto a coarse grid which by itself could not produce vortices. Finally, we discuss how concurrent integration of the nested and coarse grids can be significantly more efficient than when integrating the two grids sequentially.

31. Harris, Lucas, P H Lauritzen, and R Mittal, February 2011: A flux-form version of the conservative semi-Lagrangian multi-tracer transport scheme (CSLAM) on the cubed sphere grid. Journal of Computational Physics, 230(4), doi:10.1016/j.jcp.2010.11.001.
    [ Abstract ]

    A conservative semi-Lagrangian cell-integrated transport scheme (CSLAM) was recently introduced, which ensures global mass conservation and allows long timesteps, multi-tracer efficiency, and shape preservation through the use of reconstruction filtering. This method is fully two-dimensional so that it may be easily implemented on non-cartesian grids such as the cubed-sphere grid. We present a flux-form implementation, FF-CSLAM, which retains the advantages of CSLAM while also allowing the use of flux-limited monotonicity and positivity preservation and efficient tracer sub-cycling. The methods are equivalent in the absence of flux limiting or reconstruction filtering. FF-CSLAM was found to be third-order accurate when an appropriately smooth initial mass distribution and flow field (with at least a continuous second derivative) was used. This was true even when using highly deformational flows and when the distribution is advected over the singularities in the cubed sphere, the latter a consequence of the full two-dimensionality of the method. Flux-limited monotonicity preservation, which is only available in a flux-form method, was found to be both less diffusive and more efficient than the monotone reconstruction filtering available to CSLAM. Despite the additional overhead of computing fluxes compared to CSLAM's cell integrations, the non-monotone FF-CSLAM was found to be at most only 40% slower than CSLAM for Courant numbers less than one, with greater overhead for successively larger Courant numbers.

32. Harris, Lucas, and D R Durran, June 2010: An Idealized Comparison of One-Way and Two-Way Grid Nesting. Monthly Weather Review, 138(6), doi:10.1175/2010MWR3080.1.
    [ Abstract ]

    Most mesoscale models can be run with either one-way (parasitic) or two-way (interactive) grid nesting. This paper presents results from a linear 1D shallow-water model to determine whether the choice of nesting method can have a significant impact on the solution. Two-way nesting was found to be generally superior to one-way nesting. The only situation in which one-way nesting performs better than two-way is when very poorly resolved waves strike the nest boundary. A simple filter is proposed for use exclusively on the coarse-grid values within the sponge zone of an otherwise conventional sponge boundary condition (BC). The two-way filtered sponge BC gives better results than any of the other methods considered in these tests. Results for all wavelengths were found to be robust to other changes in the formulation of the sponge boundary, particularly with the width of the sponge layer. The increased reflection for longer-wavelength disturbances in the one-way case is due to a phase difference between the coarse- and nested-grid solutions at the nested-grid boundary that accumulates because of the difference in numerical phase speeds between the grids. Reflections for two-way nesting may be estimated from the difference in numerical group velocities between the coarse and nested grids, which only becomes large for waves that are poorly resolved on the coarse grid.