A comparative study of the performance of various vertical discretization schemes

Summary Most finite-difference numerical weather prediction models employ vertical discretizations that are staggered, and are low-order (usually second-order) approximations for the important terms such as the derivation of the geopotential from the hydrostatic equation, and the calculation of the vertically integrated divergence. In a sigma-coordinate model the latter is used for computing both the surface pressure change and the vertical velocity. All of the above-mentioned variables can diminish the accuracy of the forecast if they are not calculated accurately, and can have an impact on related quantities such as precipitation.In this study various discretization schemes in the vertical are compared both in theory and in practice. Four different vertical grids are tested: one unstaggered and three staggered (including the widely-used Lorenz grid). The comparison is carried out by assessing the accuracy of the grids using vertical numerics that range from second-order up to sixth-order.The theoretical part of the study examines how faithfully each vertical grid reproduces the vertical modes of the governing equations linearized with a basic state atmosphere. The performance of the grids is evaluated for 2nd, 4th and 6th-order numerical schemes based on Lagrange polynomials, and for a 6th-ordercompact scheme.Our interpretation of the results of the theoretical study is as follows. The most important result is that the order of accuracy employed in the numerics seems to be more significant than the choice of vertical grid. There are differences between the grids at second-order, but these differences effectively vanish as the order of accuracy increases. The sixth-order schemes all produce very accurate results with the grids performing equally well, and with the compact scheme significantly outperforming the Lagrange scheme. A second major result is that for the number of levels typically used in current operational forecast models, second-order schemes (which are used almost universally) all appear to be relatively poor, for other than the lowest modes.The theoretical claims were confirmed in practice using a large number (100) of forecasts with the Australian Bureau of Meteorology Research Centre's operational model. By comparing test model forecasts using the four grids and the different orders of numerics with very high resolution control model forecasts, the results of the theoretical study seem to be corroborated.With 8 Figures     

Interaction between atmospheric flows and obstacles: Experiments in a rotating channel

We performed an experimental study using scale models in a hydrodynamic rotating channel, concerning the interactions between fluid flows and obstacles of different shapes. The study was meant to analyze the characteristics of the wakes observed on the lee side of quasi-bidimensional obstacles, in a neutral atmosphere.The obstacles were half-cylinders (with aspect ratio 0.87), placed transversally on the channel bottom and totally submerged in the fluid. We call them quasi-bidimensional since their width was a little smaller than the channel width, thus allowing the flow to partially go round their edges.The simulations were performed in the rotating hydraulic channel of ICG-CNR in Turin, and included various conditions of rotation period and flow speed. An interesting behaviour of the wakes was found on the lee side of subsynoptic-scale obstacles, modelled in conditions of Reynolds-Rossby similitude. More precisely, if a given threshold of flow velocity is exceeded, wake size is constant and is fully determined by the height of the obstacle.     

Meso-beta scale numerical simulations of terrain drag-induced along-stream circulations. Part II: Concentration of potential vorticity within dryline bulges

Summary Hydrostatic and nonhydrostatic simulation models are employed to study the intensification of a terrain drag-induced dryline. The study develops a multi-stage theory for the evolution of the dryline including the concentration of potential vorticity accompanying meso-gamma scale dryline bulges.The numerical simulations indicate three fundamental stages of dryline intensification all of which are either directly or indirectly a result of the terrain-drag on the mid/upper-tropospheric jet stream by the Front Range of the Colorado Rocky Mountains. The first stage involves the downward momentum flux accompanying a large amplitude hydrostatic mountain wave which induces a downslope windstorm along the lee slopes. The surge of momentum (i.e., the dry, warm air associated with the downslope windstorm) propagates down the leeslope and modifies an existing weak dryline boundary. As the downslope windstorm initiates an undular bore along the lee slopes, the high momentum gradient which propagates downstream accompanying the bore, as well as the strong lower tropospheric sinking motions ahead of the bore, contract the scale of the surface moisture boundary between the dry air from above the leeslope and the moist air over the High Plains. This process further strengthens the dryline.The second stage involves the coupling of the terrain drag-induced along-stream ageostrophic front within the midtroposphere to the boundary layer through a thermally-indirect circulation. As the along-stream ageostrophic circulation intensifies within the middle troposphere down-stream from the mountain wave, sinking air parcels originating above 40 kPa descend to below 60 kPa over the High Plains where surface pressures are, only 85 kPa. These descending air parcels within the upstream branch of the along-stream ageostrophic thermally-indirect circulation contain high values of momentum and very low dewpoint values. As the planetary boundary layer (PBL) deepens due to surface warming during the morning hours, momentum and dry air from the midtropospheric along-stream ageostrophic front are entrained into the PBL. This process amplifies the bore-induced hydrostatic dryline bulge via low-level ageostrophic confluence.Finally, regions of low Richardson number (arising from strong vertical shears) within the amplifying midtropospheric along-stream ageostrophic thermally-indirect circulation become preferred regions for the development of non-hydrostatic evanescent internal gravity waves. These waves are embedded within the hydrostatic along-stream front above the low-level dryline and are accomapanied by very significant values of vertical momentum flux which act to focus the meso-gamma scale structure of the dryline into smaller scale bulges where low-level winds and vorticities are very high. This meso-gamma scale process follows the hydrostatic tilting and vortex tube stretching which creates meso-beta scale maxima of mid-lower tropospheric vorticity. The turbulent momentum fluxes accompanying wavebreaking within the nonhydrostatic dryline bulge create very large (i.e., stratospheric values of) potential vorticity near 70 kPa due to the nonconservation of potential vorticity on isentropic surfaces.With 30 Figures     

Fossil-pollen evidence for abrupt climate changes during the past 18 000 years in eastern North America

A quantitative measure of the rate at which fossil-pollen abundances changed over the last 18 000 years at 18 sites spread across eastern North America distinguishes local from regionally synchronous changes. Abrupt regional changes occurred at most sites in late-glacial time (at 13700, 12 300, and 10000 radiocarbon yr BP) and during the last 1000 years. The record of abrupt late-glacial vegetation changes in eastern North America correlates well with abrupt global changes in ice-sheet volume, mountain snow-lines, North Atlantic deep-water production, atmospheric CO₂, and atmospheric dust, although the palynological signal varies from site to site. Changes in vegetation during most of the Holocene, although locally significant, were not regionally synchronous. The analysis reveals non-alpine evidence for Neoglacial/Little Ice Age climate change during the last 1000 years, which was the only time during the Holocene when climate change was of sufficient magnitude to cause a synchronous vegetational response throughout the subcontinent. During the two millennia preceding this widespread synchronous change, the rate of change at all sites was low and the average rate of change was the lowest of the Holocene.Contribution to Clima Locarno Past and Present Climate Dynamics; Conference September 1990, Swiss Academy of Sciences — National Climate Program     

Nutrient-chlorophyll trajectories across trophic gradients

We estimate the response of chl-a (mg · m^–3) to changes in concentrations of total phosphorus (TP) by calculating the slopeS = chl-a/TP in chl-a =f(TP) graphs. Results show that in years where algae are P-limited oligotrophic lakes respond less (median slope 0.21) to changes in nutrient concentrations than eutrophic lakes, (median slope 0.31) and these again less than hypereutrophic lakes, (median slope 1.02). We find no saturation value for the slope within the TP range considered (6–480 mg · m^–3). Chl-a in eutrophic lakes responds more frequently to non-nutrient factors than oligotrophic and hypereutrophic lakes. Results obtained by replacing TP with a new nutrient parameter, TP = 0.056 · TP · IN^0.226, in which inorganic nitrogen, IN, is factored in, suggest that nitrogen has an influence on chl-a in oligotrophic lakes. Blue-green algae respond less to changes in TP than other algal species, e.g., diatoms.     

Fractional Crystallization and Liquid Immiscibility Processes in the Alkaline-Carbonatite Complex of Juqui (So Paulo, Brazil)

The Juqui circular intrusion, which is Cretaceous in age (130–135Ma), crops out in the Precambrian gneissic basement in Brazilover an area of 14 km2. It consists of olivine clinopyroxen-itecumulates (with minor olivine gabbros) in the northeastern sector(74 vol.%), whereas ijolites-melteigites-urtites (4%) and nephelinesyenites with minor essexites and syenodiorites (21%) outlinesubannular concentric patterns with an Mg-carbonatite core (1%), in the southwestern part of the complex. Petrographical, bulk rock, and mineral compositional trendsindicate that the origin of the complex can be largely accountedfor by shallow-level fractional crystallization of a carbonatedbasanitic parental magma. Such a magma was generated deep inthe subcontinental lithosphere by low-degree partial meltingof a garnet-phlogopite peridotite source. Mass-balance calculations in agreement with field volume estimatespermit definition of several fractionation stages of the magmaticevolution under nearly closed-system conditions, with inwarddevelopment of zonally arranged side-wall cumulates. These stagesinvolved: (1) fractionation from basanite to essexite magma(liquid fraction F = 33–5%) by crystallization of olivineclinopyroxenite plus minor olivine alkali gabbro cumulates;(2) derivation of the least differentiated mafic nepheline syenite(F = 5–5 %) from essexitic magma by subtraction of a syenodioriteassemblage; (3) exsolution of a carbonatite liquid (5%) froma CO₂-enriched mafic nepheline syenite magma, which also underwentcontinuous fractionation giving rise to ijolite-melteigite-urtitecumulates. The proportion of cumulus clinopyroxene and biotiteand intercumulus nepheline and alkali feldspar in these lastrocks, as well as the absence of alkalis in carbonatite, maybe attributed, at least in part, to loss of alkali-rich hydrousfluids released during and after the unmixing formation of thetwo conjugate liquids. The KD values determined for Mg-carbonatite/nepheline syeniteare lower (1–4–2–9) for light rare earth elements(LREE) than for REE from Eu to Yb (4–6–7–8),in contrast to recent experimental results (Hamilton et al.,1989). A possible explanation is that Juquia Mg-carbonatiterepresents an alreadydifferentiated magma, which underwent extensivefractionation of LREE-enriched calcite. In this way, the highvariability of K₀ REE patterns observed in several alkaline-carbonatitecomplexes can also be accounted for. The remarkably constant initial ⁸⁷Sr/⁸⁶Sr ratios (mostly between0–7052 and 0–7057) support the interpretation ofthe intrusion as having been generated by fractrional crystallizationand liquid immiscibility from a common parental magma. Iligherisotopic ratios (0–7060–0–7078), found mainlyin dykes and in the border facies of the intrusion, may be dueto contamination by the gecissic basement.     

Thermal expansion and spontaneous strain associated with the normal-incommensurate phase transition in melilites

The linear thermal expansions of åkermanite (Ca₂MgSi₂O₇) and hardystonite (Ca₂ZnSi₂O₇) have been measured across the normal-incommensurate phase transition for both materials. Least-squares fitting of the high temperature (normal phase) data yields expressions linear in T for the coefficients of instantaneous linear thermal expansion, $$\alpha _1 = \frac{1}{l}\frac{{dl}}{{dT}}$$ for åkermanite: $$\begin{gathered} \alpha _{[100]} = 6.901(2) \times 10^{ - 6} + 1.834(2) \times 10^{ - 8} T \hfill \\ \alpha _{[100]} = - 2.856(1) \times 10^{ - 6} + 11.280(1) \times 10^{ - 8} T \hfill \\ \end{gathered} $$ for hardystonite: $$\begin{gathered} \alpha _{[100]} = 15.562(5) \times 10^{ - 6} - 1.478(3) \times 10^{ - 8} T \hfill \\ \alpha _{[100]} = - 11.115(5) \times 10^{ - 6} + 11.326(3) \times 10^{ - 8} T \hfill \\ \end{gathered} $$ Although there is considerable strain for temperatures within 10° C of the phase transition, suggestive of a high-order phase transition, there appears to be a finite ΔV of transition, and the phase transition is classed as “weakly first order”.     

Structure of the αFexAl1:xOOH solid solution

The three-dimensional local organisation around Fe atoms in a natural diaspore (Al_0.9955Fe_0.0045OOH) has been investigated by angular measurements of X-ray absorption spectra. It is demonstrated that in a single crystal of diaspore, the absorption cross-section exhibits the special case of trichroism where three independent measurements are needed to determine the absorption cross-section for any direction of polarization. Extended X-ray absorption fine structure (EXAFS) spectra were thus recorded at the following orientations of the polarization vector: , , and . The incoming white beam was monochromatized using two Si(331) crystals, which deliver at the Fe K-edge a completely linearly polarized X-ray beam. The reliability of our measurements was checked by comparing the isotropic EXAFS spectrum calculated from the three orthogonal measurements to the one of the diaspore powder recorded at the magic angle. It is shown that Fe³⁺ ions are not randomly distributed within the diaspore framework. Furthermore, only part of the Fe³⁺ ions substitutes Al, the others being located in the channels of the structure. The 3D local structure of the Fe domains has been modeled assuming hematite-like clusters of three Fe octahedra topotactically grafted to aluminous chains. These Fe clusters are thought to represent ancient multinuclear Fe surface complexes having formed at the time of the diaspore growth, and being sealed in its bulk structure. The whole crystal of diaspore is then thought to have kept the memory of the heterogeneous nucleation mechanism of these hematite nuclei. In addition to the well-known examples of atom segregations, ion vacancies, and intergrowths of discrete phases, this new type of crystal defect represents another evidence of non-equilibrium crystallization process under the thermodynamic and kinetic conditions that prevail at the earth's surface.     

Using numerical modelling to evaluate tsunami hazard near the Kuril Island

A sequence of computer experiments is used to study questions concerning the tsunami problem as a quantitative estimate of tsunami danger, detailed geographical tsunami classification, determination of the parameters of critical tsunami waves, and the conditions of their development. We call a wave critical, if its impact on the coast is most hazardous.Using the Middle Kuril Island as an example, we present the results of a computer experiment which includes determining the wavefields on the shelf and estimating the effects connected with the deep-water Bussol and Diana Straits.Numerical simulation of tsunami waves of different sources permits the assessment of the extent of tsunami danger in different areas of the coastal zone of Simushir Island, depending on the location of the focus zone and their geometry.The major singularities of the wavefield arise in the zones of the deep-water straits. The distribution of the amplification factors is determined by both the global parameters of the wavefields and the local properties of individual harbours. The results obtained for a particular harbour in the northern part of Simushir Island, formed the basis for the quantitative estimate of tsunami danger for this area.     

Synthesis and stability of bastnaesites in a part of the system (Ce,La)-F-H-C-O

Summary Bastnaesites of Ce and La and their OH-analogs were synthesized and their stability relations were determined atPf = 1 kbar andT = 400 to 900°C in a part of the system (Ce,La)-F-H-C-0. The initial fluid compositions were such that and HF/(HF + H₂O) ratios were 0 to 0.172. XRD and IR studies indicate that bastnaesites equilibrated in initial fluids low in HF are all F-enriched. The hydroxylbastnaesite-(La) is stable up to 810°C and the fluorbastnaesite-(La) is stable up to 860°C. Their condensed breakdown products are La₂O₂CO₃ and LaOF, respectively. The stability of Ce bastnaesites is slightly dependent. The hydroxylbastnaesite-(Ce) is stable up to 660°C at the defined by the IQF buffer and up to 640°C by the MH buffer. The fluorbastnaesite-(Ce) is stable up to 800°C at the defined by the IQF and up to 760°C by the MH buffer. The condensed breakdown product for the hydroxyl end-member is simply CeO₂ but for the fluorine one is a combination of CeO₂, CeF₃, and CeOF. Factors, such as OH vs F, , and bulk composition, that affect the stability of individual species are discussed. Petrogenic implications resulting from the present study include that bastnaesites can be stable from hydrothermal to magmatic conditions, that F-enriched species can form in an environment relatively low in F content, and that OH-species are rare and occur only in low-temperature environments essentially devoid of F.

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Synthese und Stabilität von Bastndsil in einem Teil des Systems (Ce,La)-F-H-C-O

Zusammenfassung Ce- und La-Bastnäsite, sowie deren OH-Analoga wurden synthetisiert und ihre Stabilitätsbeziehunger beiP _f = 1 kbar undT = 400 bis 900°C wurden im System (Ce,La)F-H-C-O bestimmt. Die anfänglichen Flüssigkeitszusammensetzungen waren so, daß und die HF/(HF + H₂O)-Verhältnisse 0–0.172 waren. Röntgenpulver- und Ultrarot-Untersuchungen zeigten, daß Bastnäsite, die mit anfänglich HF-armen Flüssigkeiten equilibriert wurden, alle an F angereichert sind. Hydroxilbastndsit-(La) ist bis 810°C und Fluorbastnäsit-(La) bis 860°C stabil. Ihre festen Zersetzungsprodukte sind La₂O₂O₃, bzw. LaOF. Die Stabilität der Ce-Bastnäsite hängt etwas von ab. Hydroxilbastnäsit-(Ce) ist bei des Eisen-Quarz-Fayalit-Puffers bis 660°C stabil und mit Magnetit-Hämatit-Puffer bis 640°C. Das feste Zerfallsprodukt ist für das Hydroxil-Glied nur CeO₂, für das Fluor-Glied eine Mischung aus CeO₂, CeF₃ und CeOF. Faktoren, welche die Stabilität der einzelnen Spezies beeinflussen, werden diskutiert, wie das Verhältnis OH zu F, und die Gesamtzusammensetzung. Petrogenetische Folgerungen aus der vorliegenden Studie schließen ein, daß Bastnäsite von hydrothermalen bis zu magmatischen Bedingungen stabil sein können, daß sich an F angereicherte Glieder in relativ F-armer Umgebung bilden können, und daß OH-Glieder selten sind und nur unter Bildungsbedingungen niedriger Temperatur und weitgehender Abwesenheit von F auftreten.

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With 8 Figures