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AbstractsNew techniques have been developed for atomic self-consistent-field calculations by numerica integration. For the origin and tail regions we present analytical expansions which can represent thi solutions to high accuracy. For the numerical integration in the central region a five-point generaliza tion of the Numerov formula is used; the error term is of the order h l o . While this formula is unstable i used in the customary way, stability is achieved by using a Gaussian elimination technique. The nev procedures are tested on the ground state of the helium isoelectronic series; with 251 integratior points all quantities are calculated with an inherent accuracy of better than lo-".Des mtthodes nouvelles pour des calculs atomiques de type SCF par inttgration numtrique ont ttt developpbes. Pour les rtgions ou r e s t trbs grand ou trbs petit nous prtsentons des dtveloppementi analytiques, qui peuvent reprtsenter les solutions avec grande precision. Pour I'inttgration numtriqur dans la region centrale une gtntralisation de la formule de Numerov a cinq points a e t t utiliste; le terme d'erreur est de I'ordre h". Cette formule est instable si on l'utilise d'une facon conventionnelle mais on peut atteindre un proctdt stable par une Climination Gaussienne. Les proctdts nouveaux ont CtC testts pour I'ttat fondamental de la sirie isotlectronique a I'atome de helium. Avec 251 points d'integration toutes les quantitts considtries sont obtenues avec une prtcision inhtrente de meilleur de lo-".Neue Methoden fur atomare SCF-Berechnungen durch numerische Integration sind entwickelt worden. Fur die Koordinatenursprungs-und Schwanzbereiche werden analytische Entwicklungen vorgelegt, die die Lasungen mit hoher Genauigkeit reprasentieren konnen. Fur die numerische Integration im Zentralbereich wird eine Funfpunkteverallgemeinerung der Numerov'schen Formel verwendet, in welcher das Fehlerglied von der Ordnung h" ist. Diese Formel ist instabil, wenn sie in der iiblichen Weise angewandt wird; Stabilitat kann aber durch ein Gauss'sches Eliminationsverfahren erreicht werden. Die neuen Methoden werden auf den Grundzustand der zu He isoelektronischen Reihe getestet. Mit 25 1 Integrationspunkten werden alle hier betrachteten Grossen mit einer eigenen Genauigkeit besser als lo-" erhalten.

To determine how well a low-order wavenumber representation describes a hurricane wind speed field, given its natural variability in space and time, low-order wavenumber representations were calculated for hourly “snapshots” of the 10-m wind speed field generated by the current operational hurricane model. Two distinct periods were examined: the first when the storm is in a reasonably steady state over 7–8 h and the second where the storm is changing its internal structure over a similar time interval. Observing system sensitivity experiments were also performed using wind speed field time series obtained from interpolation of the model snapshots for each of the two periods. The time series were sampled along the flight legs of a typical “figure four” aircraft flight pattern to simulate the surface wind data collection process to ascertain the effects of the wind speed field’s temporal and spatial variability upon the low-order wavenumber analyses. The comparison between the model wind speed field at any time and the wavenumber representations during the “steady state” period shows that the essential features of the wind speed field are captured by wavenumbers 0 and 1 and that including up to wavenumber 3 practically reproduces the model field. However, in the “nonsteady” period the wavenumber 0 and 1 representation is frequently unable to capture the essential characteristics of the wind speed field. The observing system sensitivity experiments suggest that when the primary circulation is rapidly changing in amplitude and/or structure during the data collection period, the low-order wavenumbers analysis of the wind speed field will only represent the temporal mean structure.

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