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"Hall, David M."
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Competing against luck : the story of innovation and customer choice
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An Energy Consistent Discretization of the Nonhydrostatic Equations in Primitive Variables
We derive a formulation of the nonhydrostatic equations in spherical geometry with a Lorenz staggered vertical discretization. The combination conserves a discrete energy in exact time integration when coupled with a mimetic horizontal discretization. The formulation is a version of Dubos and Tort (2014, https://doi.org/10.1175/MWR-D-14-00069.1) rewritten in terms of primitive variables. It is valid for terrain following mass or height coordinates and for both Eulerian or vertically Lagrangian discretizations. The discretization relies on an extension to Simmons and Burridge (1981, https://doi.org/10.1175/1520-0493(1981)109<0758:AEAAMC>2.0.CO;2) vertical differencing, which we show obeys a discrete derivative product rule. This product rule allows us to simplify the treatment of the vertical transport terms. Energy conservation is obtained via a term‐by‐term balance in the kinetic, internal, and potential energy budgets, ensuring an energy‐consistent discretization up to time truncation error with no spurious sources of energy. We demonstrate convergence with respect to time truncation error in a spectral element code with a horizontal explicit vertically implicit implicit‐explicit time stepping algorithm. Plain Language Summary Energy consistent discretizations have proven useful in guiding the development of numerical methods for simulating fluid dynamics. They ensure that the discrete method does not have any spurious sources of energy, which can lead to unstable and unrealistic simulations. Here we provide an energy consistent discretization of the equations used by global models of the Earth's atmosphere. The discretization is written in terms of standard variables in spherical coordinates and supports a wide variety of terrain following vertical coordinates. It can be used with any horizontal discretization that has a discrete version of the integration‐by‐parts identity. Key Points We give a discrete Hamiltonian formulation of the nonhydrostatic equations in primitive variables The formulation supports mass or height terrain following coordinates The Lorenz staggered vertical discretization obeys a derivative product rule
Journal Article
DCMIP2016: the splitting supercell test case
This paper describes the splitting supercell idealized test case used in the 2016 Dynamical Core Model Intercomparison Project (DCMIP2016). These storms are useful test beds for global atmospheric models because the horizontal scale of convective plumes is O(1 km), emphasizing non-hydrostatic dynamics. The test case simulates a supercell on a reduced-radius sphere with nominal resolutions ranging from 4 to 0.5 km and is based on the work of . 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 the 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 0.5 km resolution, although exploratory simulations at 0.25 km imply some dynamical cores require more refinement to fully converge. 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 regimes.
Journal Article
Discontinuous Galerkin Transport on the Spherical Yin–Yang Overset Mesh
A discontinuous Galerkin (DG) transport scheme is presented that employs the Yin–Yang grid on the sphere. The Yin–Yang grid is a quasi-uniform overset mesh comprising two notched latitude–longitude meshes placed at right angles to each other. Surface fluxes of conserved scalars are obtained at the overset boundaries by interpolation from the interior of the elements on the complimentary grid, using high-order polynomial interpolation intrinsic to the DG technique. A series of standard tests are applied to evaluate its performance, revealing it to be robust and its accuracy to be competitive with other global advection schemes at equivalent resolutions. Under p-type grid refinement, the DG Yin–Yang method exhibits spectral error convergence for smooth initial conditions and third-order geometric convergence for C1 continuous functions. In comparison with finite-volume implementations of the Yin–Yang mesh, the DG implementation is less complex, as it does not require a wide halo region of elements for accurate boundary value interpolation. With respect to DG cubed-sphere implementations, the Yin–Yang grid exhibits similar accuracy and appears to be a viable alternative suitable for global advective transport. A variant called the Yin–Yang polar (YY-P) mesh is also examined and is shown to have properties similar to the original Yin–Yang mesh while performing better on tests with strictly zonal flow.
Journal Article
Soil Management Systems to Overcome Multiple Constraints for Dryland Crops on Deep Sands in a Water Limited Environment on the South Coast of Western Australia
Deep sands on the south coast sandplain of Western Australia (WA) have multiple soil constraints including water repellence, high soil strength, low nutrient levels and subsoil acidity. The aim of the study was to test contrasting methods of managing water repellence and to assess their impacts on one or more soil constraints to crop production. These methods included seeding tyne design (knife point, winged points, paired row), soil wetting agent addition, strategic inversion tillage (rotary spading, mouldboard ploughing to 0.35 m) and clay-rich subsoil addition (170 t ha−1 with incorporation by spading to 0.20 or 0.35 m). Limesand (2 t ha−1) was applied as a split plot treatment prior to tillage. Cumulative crop yields were increased by 2.1–2.6 t ha−1 over five years by the strategic deep tillage and clay application treatments compared to the control. Water repellence was reduced by the inversion ploughing and subsoil clay addition treatments only. The effect of water repellence on crop establishment was expressed only in low rainfall years (Decile < 4) and mitigated by the paired row, wetting agent, spader and clay-amended treatments. In all years, plant numbers were adequate to achieve yield potential regardless of treatment. Soil K and plant tissue K and B were increased where clay had been applied. Inversion tillage reduced soil pH, organic carbon (OC) and macro nutrients in the 0–0.1 m layer although in most years there was no significant decline in plant tissue macro nutrient levels. Soil strength was reduced as a result of the inversion tillage to a depth of 0.35 m. However, the alleviation of soil strength and the crop yield responses diminished with time due to re-compaction. No crop response to the applied lime was found over five years at this site since the soil pHCaCl2 exceeded 4.7 within the root zone. In terms of soil constraints, we conclude that compaction was the dominant constraint at this site followed by water repellence and K deficiency.
Journal Article
Short- and Long-Term Effects of Lime and Gypsum Applications on Acid Soils in a Water-Limited Environment: 2. Soil Chemical Properties
Soil acidity or aluminum (Al) toxicity is a major limitation to crop production. In this paper, we examine the effects of surface-applied lime and gypsum on soil profile chemical properties that affect Al toxicity in short-term (1 year), medium-term (2 years and 8 months) and long-term (10 years) experiments. Sulfate applied to the soil surface as gypsum was leached rapidly to a depth of 40 cm in the short-term despite relatively low amounts (279 mm) of rainfall. In the medium and long-term experiments, 28–54% of the sulfate applied as gypsum was retained in the 0–50 cm soil layer due to adsorption and precipitation reactions. The combined application of lime and gypsum increased soil calcium, to a depth of 30 cm in the short-term and to a depth of 50 cm in the medium and long-terms. Increases in soil sulfate and calcium were associated with greater electrical conductivity to a depth of 50 cm for all sampling times. Application of lime alone had no impact on soil Al, pH, and calcium in the soil layers below 10 cm in the short and medium terms. In the long-term, increasing the rate of lime application from 2 to 8 t L ha−1 increased soil pH in the 10–20 cm soil layer while soil Al decreased to a depth of 30 cm. The combined use of lime and gypsum decreased soil Al in the 30–50 cm soil layer in the medium-term and the 20–30 cm soil layer in the long-term which was more than when only lime was applied. Hence, we recommend the use of lime plus gypsum for treating soils with subsoil Al toxicity. Additionally, soil Al measurements are a more sensitive measurement of the impact of surface application lime and lime plus gypsum than soil pH.
Journal Article
Short- and Long-Term Effects of Lime and Gypsum Applications on Acid Soils in a Water-Limited Environment: 3. Soil Solution Chemistry
Aluminum (Al) toxicity imposes a significant limitation to crop production in South Western Australia. This paper examines the impact of surface-applied lime and gypsum on soil solution chemistry in the short term (1 year) and the long-term (10 years) in water limited environments. In the experiments, we measured soil solution chemistry using a paste extract on soil profile samples collected to a depth of 50 cm. We then used the chemical equilibrium model MINTEQ to predict the presence and relative concentrations of Al species that are toxic to root growth (Al associated with Al3+ and AlOH2 or Toxic-Al) and less non-toxic forms of Al bound with sulfate, other hydroxide species and organic matter. A feature of the soils used in the experiment is that they have a low capacity to adsorb sulfate. In the short term, despite the low amount of rainfall (279 mm), sulfate derived from the surface gypsum application is rapidly leached into the soil profile. There was no self-liming effect, as evidenced by there being no change in soil solution pH. The application of gypsum, in the short term, increased soil solution ionic strength by 524–681% in the 0–10 cm soil layer declining to 75–109% in the 30–40 cm soil layer due to an increase in soil solution sulfate and calcium concentrations. Calcium from the gypsum application displaces Al from the exchange sites to increase soil solution Al activity in the gypsum treatments by 155–233% in the short term and by 70–196% in the long term to a depth of 40 cm. However, there was no effect on Toxic-Al due to Al sulfate precipitation. In the long term, sulfate leaching from the soil profile results in a decline in soil solution ionic strength. Application of lime results in leaching of alkalinity into the soil profile leading to a decreased Toxic-Al to a depth of 30 cm in the long term, but it did not affect Toxic-Al in the short term. Combining an application of lime with gypsum had the same impact on soil solution properties as gypsum alone in the short term and as lime alone in the long term.
Journal Article
Short- and Long-Term Effects of Lime and Gypsum Applications on Acid Soils in a Water-Limited Environment: 1. Grain Yield Response and Nutrient Concentration
Surface (0–10 cm) and subsoil (soil layers below 10 cm) acidity and resulting aluminum (Al) toxicity reduce crop grain yields. In South Western Australia (SWA), these constraints affect 14.2 million hectares or 53% of the agricultural area. Both lime (L, CaCO3) and gypsum (G, CaSO4) application can decrease the toxic effect of Al, leading to an increase in crop grain yields. Within the region, it is unclear if G alone or the combined use of L and G has a role in alleviating soil acidity in SWA, due to low sulfate S (SO4–S) sorption properties of the soil. We present results from three experiments located in the eastern wheatbelt of SWA, which examined the short-term (ST, 2 growing seasons), medium-term (MT, 3 growing seasons), and long-term (LT, 7 growing seasons over 10 years) effects of L and G on grain yield and plant nutrient concentrations. Despite the rapid leaching of SO4–S and no self-liming impact, it was profitable to apply G, due to the significant ST grain yield responses. The grain yield response to G developed even following relatively dry years, but declined over time due to SO4–S leaching. At the LT experimental site had received no previous L application, whereas, at the ST and MT sites, L had been applied by the grower over the previous 5–10 years. For the LT site, the most profitable treatment for wheat (Triticum aestivum L.) grain yield, was the combined application of 4 t L ha−1 with 2 t G ha−1. At this site, the 0–10 cm soil pHCaCl2 was 4.6, and AlCaCl2 was greater than 2.5 mg kg−1 in the 10–30 cm soil layer. In contrast, at the ST and MT sites, the pHCaCl2 of 0–10 cm soil layer was ≥5.5; it was only profitable to apply G to the MT site where the soil compaction constraint had been removed by deep ripping. The use of L increases soil pHCaCl2, resulting in the improved availability of anions, phosphorus (P) in the LT and molybdenum (Mo) at all sampling times, but reduced availability of cations zinc (Zn) in the LT and manganese (Mn) at all sampling. The application of G reduced Mo concentrations, due to the high SO4–S content of the soil.
Journal Article
DCMIP2016: a review of non-hydrostatic dynamical core design and intercomparison of participating models
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.
Journal Article