Review of numerical methods for nonhydrostatic weather prediction models

Summary ?Currently available computer power allows to run operational numerical weather prediction models at resolutions higher than 10 km. The aim of such high resolution modeling is the prediction of local weather, including orographically induced winds and local precipitation patterns. In this range the hydrostatic approximation is no longer valid and nonhydrostatic models have to be used instead. For several decades these models have been developed for research purposes only, but operational application is now reality. In this paper, the numerical methods used in current nonhydrostatic forecast models will be reviewed and some promising techniques in this field will be discussed. Special attention is given to aspects such as the choice of the vertical coordinate, the efficiency of algebraic solvers for semi-implicit time discretizations, and accurate and non-oscillatory advection schemes. Received July 6, 2001; revision October 12, 2001     

Intercomparison of Stratospheric Chemistry Models under Polar Vortex Conditions

Several stratospheric chemistry modules from box, 2-D or 3-D models, have been intercompared. The intercomparison was focused on the ozone loss and associated reactive species under the conditions found in the cold, wintertime Arctic and Antarctic vortices. Comparisons of both gas phase and heterogeneous chemistry modules show excellent agreement between the models under constrained conditions for photolysis and the microphysics of polar stratospheric clouds. While the mean integral ozone loss ranges from 4–80% for different 30–50 days long air parcel trajectories, the mean scatter of model results around these values is only about ±1.5%. In a case study, where the models employed their standard photolysis and microphysical schemes, the variation around the mean percentage ozone loss increases to about ±7%. This increased scatter of model results is mainly due to the different treatment of the PSC microphysics and heterogeneous chemistry in the models, whereby the most unrealistic assumptions about PSC processes consequently lead to the least representative ozone chemistry. Furthermore, for this case study the model results for the ozone mixing ratios at different altitudes were compared with a measured ozone profile to investigate the extent to which models reproduce the stratospheric ozone losses. It was found that mainly in the height range of strong ozone depletion all models underestimate the ozone loss by about a factor of two. This finding corroborates earlier studies and implies a general deficiency in our understanding of the stratospheric ozone loss chemistry rather than a specific problem related to a particular model simulation.     

Meso-gamma scale forecasts using the nonhydrostatic model LM

Summary ?The nonhydrostatic model LM was developed for small scale operational predictions. Advances in computer development will give the possibility of operational models of a rather fine scale, which will cover the meso-gamma scale. The LM is currently applied at a scale of 7 km and an increase of the operational resolution to 2.5 km is planned for the next few years. Predictions of such high resolution require to abandon the hydrostatic assumption, which is used with most current operational weather prediction models. The LM was designed to cover all resolutions from 50 m to 50 km with an efficiency making it suitable for operational use. It is a fully elastic model, using second order centred finite differences. The time integration is done using the Klemp–Wilhelmson method, treating the slow modes by a larger time step than the fast modes. The vertical propagation of the fast waves is done implicitly. After describing the design of the LM, this paper gives examples of model predictions at the meso-γ scale. Some results of the current operational application at the resolution 7 km are presented. Deficiencies in the localisation of model generated precipitation are investigated using an idealised bell shaped mountain and applying different resolutions. In this way the convergence to the correct solution can be investigated. From these results it is concluded, that orographic filtering is necessary and the effect of such filtering on precipitation forecasts is investigated. Finally, the prediction of a squall line over northern Germany is shown in order to demonstrate the potential of the model in forecasting the meso-γ scale. Received May 15, 2001; revised September 21, 2001     

Exhumed fault-bounded Alpine blocks along the Periadriatic lineament: the Eder unit (Carnic Alps, Austria)

The Eder unit in the Carnic Alps, which is situated immediately south of the Periadriatic lineament (PL), represents a fault-bounded block consisting of a low-grade (up to 400?°C, indicated by epizonal illite “crystallinity” values, recrystallized quartz, and non-recrystallized white mica) metamorphic Paleozoic metasedimentary sequence. Until now, it has been assumed to represent a separate Variscan nappe. The rocks of the Eder unit show a strong E- to W-oriented stretching lineation on steep foliation planes (D₁) subparallel to the PL. D₁ structures originated near the temperature peak of metamorphism, and shear sense indicators show dextral ductile shear parallel to the PL. Tight mesoscale D₂ folds formed on the cooling path. K–Ar and Ar–Ar ages from newly formed white mica cluster around 32–28 and 18–13 Ma and suggest a two-stage Tertiary history of the Eder unit. We interpret the Eder unit as a fault-bounded block formed during Oligocene large-scale dextral shearing along the PL (near T_max) and exhumed in mid-Miocene times during another phase of activity along the PL. Its nature as a separate Variscan nappe is questioned.     

Phase-array decomposition of a seismic section

A seismic re fraction/wide-angle reflection profile is analysed for the presence of correlated events ('phases'). The correlation problem is formulated in terms of temporally, spatially and frequency-local complex covariances. For robustness, the method concentrates on phase rather than amplitude information. This allows a computationally efficient algorithm that can make allowance for signal correlation length and can model curved wavefronts. A statistical test based on residual phase misfit across the analysed subarray is used to assess the probability that a detected event represents a real correlated signal.
With our chosen analysis parameters and confidence level (over 99.9 per cent). 1222 events were detected in the data. Using simple techniques based on 1-D earth models, detected events are associated with a small number of particular wave types. In this way, we have succeeded in classifying almost 95 per cent of the detected events. Those that remain describe those components of the data that are inconsistent with our simple ray paths in the 1-D assumption and with our prescribed tolerance. These include reverberations, near-surface guided waves and reflected waves from strongly laterally inhomogeneous structures. According to our modelling, about 25 per cent of the detected events are consistent with simple P -wave reflected energy, and these are to a very large extent (over 85 per cent) distinct from all the other wave-type models we have used. A direct mapping of the detected events into the offset-depth domain reveals dear internal and external consistencies among the detections for the various wave types. Estimated earth structure is consistent with models from previous analyses based on much larger data sets.
We have thus succeeded in extracting correlated events from the data and decomposing these, approximately but meaningfully, into distinct classes (ray paths)     

Stratigraphy of the upper cretaceous and lower tertiary strata in the Tethyan Himalayas of Tibet (Tingri area,China)

The 1500-m-thick marine strata of the Tethys Himalaya of the Zhepure Mountain (Tingri, Tibet) comprise the Upper Albian to Eocene and represent the sedimentary development of the passive northern continental margin of the Indian plate. Investigations of foraminifera have led to a detailed biozonation which is compared with the west Tethyan record. Five stratigraphic units can be distinguished: The Gamba group (Upper Albian - Lower Santonian) represents the development from a basin and slope to an outer-shelf environment. In the following Zhepure Shanbei formation (Lower Santonian - Middle Maastrichtian), outer-shelf deposits continue. Pebbles in the top layers point to beginning redeposition on a continental slope. Intensified redeposition continues within the Zhepure Shanpo formation (Middle Maastrichtian - Lower Paleocene). The series is capped by sandstones of the Jidula formation (Danian) deposited from a seaward prograding delta plain. The overall succession of these units represents a sea-level high at the Cenomanian/Turonian boundary followed, from the Turonian to Danian, by an overall shallowing-upward megasequence. This is followed by a final transgression — regression cycle during the Paleocene and Eocene, documented in the Zhepure Shan formation (?Upper Danian - Lutetian) and by Upper Eocene continental deposits. The section represents the narrowing and closure of the Tethys as a result of the convergence between northward-drifting India and Eurasia. The plate collision started in the Lower Maastrichtian and caused rapid changes in sedimentation patterns affected by tectonic subsidence and uplift. Stronger subsidence and deposition took place from the Middle Maastrichtian to the Lower Paleocene. The final closure of remnant Tethys in the Tingri area took place in the Lutetian.     

The Silurian of Gotland (Sweden): facies interpretation based on stable isotopes in brachiopod shells

The Silurian of Gotland, Sweden, consists of 440 m of carbonate deposits. Repeatedly, uniform sequences of micritic limestones and marls are interrupted by complex-structured reefs and by adjacent platform sediments. Generally, the alteration of facies is interpreted as the result of sea-level fluctuations caused by a gradual regression with superimposed minor transgressive pulses. The purpose of this study is a facies interpretation based on both field observations and stable isotope measurements of brachiopod shells. Approximately 700 samples from stratigraphically arranged localities in different facies areas have been investigated. The carbon and oxygen isotopes show principally parallel curves and a close relationship to the stratigraphic sequence. Lower values occur in periods dominated by deposition of marly sequences. Higher values are observed in periods dominated by reefs and extended carbonate platforms. The oxygen isotope ratios are interpreted to reflect paleosalinity changes due to varying freshwater input, rather than to paleotemperature. Carbon isotope ratios are believed to have been connected to global changes in the burial of organic carbon in black shales during periods of euxinic deep water conditions. Consequently, the facies succession on Gotland results from global paleoclimatic conditions. Changes in terrigenous input due to different rates of weathering and freshwater runoff, rather than sea-level fluctuations, control the carbonate formation of the Silurian on Gotland.     

Accretion and exhumation at a Variscan active margin, recorded in the Saxothuringian flysch

The Saxothuringian flysch basin, on the north flank of the Central European Variscides, was fed and eventually overthrust by the northwestern, active margin of the Tepla-Barrandian terrane. Clast spectra, mineral composition and isotopic ages of detrital mica and zircon have been analyzed in order to constrain accretion and exhumation of rocks in the orogenic wedge. The earliest clastic sediments preserved are of early Famennian age (ca. 370?Ma). They are exposed immediately to the NW of the suture, and belong to the par-autochthon of the foreland. Besides ultramafic (?ophiolite) material, these rocks contain clasts derived from Early Paleozoic continental slope sediments, originally deposited at the NW margin of the Saxothuringian basin. These findings, together with the paleogeographic position of the Famennian clastics debris on the northwestern passive margin, indicate that the Saxothuringian narrow ocean had been closed by that time. Microprobe analyses of detrital hornblendes suggest derivation from the “Randamphibolit” unit, now present in the middle part of the Saxothuringian allochthon (Münchberg nappes). Detrital zircons of metamorphic rocks formed a little earlier (ca. 380?Ma) indicate rapid recycling at the tectonic front. The middle part of the flysch sequence (ca. early to middle Viséan), both in the par-autochthon and in the allochthon, contains abundant clasts of Paleozoic rocks derived from the northwestern slope and rise, together with debris of Cadomian basement, 500-Ma granitoids and 380?Ma (early Variscan) crystalline rocks. All of these source rocks were still available in the youngest part of the flysch (c. middle to late Viséan), but some clasts record, in addition, accretion of the northwestern shelf. Our findings permit deduction of minimum rates of tectonic shortening well in excess of 10–30?mm per year, and rates of exhumation of ca. 3?mm/a, and possibly more.