Cokriging nonstationary data

Universal cokriging is used to obtain predictions when dealing with multivariate random functions. An important type of nonstationarity is defined in terms of multivariate random functions with increments which are stationary of orderk. The covariance between increments of different variables is modeled by means of the pseudo-cross-covariance function. Criteria are formulated to which the parameters of pseudo-cross-covariance functions must comply so as to ensure positive-definiteness. Cokriging equations and the induced cokriging equations are given. The study is illustrated by an example from soil science.     

Spatial variability and interpolation of daily precipitation amount

Daily precipitation amounts show spatial variation over sub-continential regions. Point measurements, representative for regions of land, have to be interpolated towards unobserved locations. In this study four days in 1984 were selected to investigate the spatial variability of daily precipitation amount in North-western Europe in relation to the meteorological conditions. Data were interpolated using Kriging. Crossvalidation was used to compare interpolated values with measured values. Large differences in the spatial structure of daily precipitation amount are obsered as a result of different meterological conditions. Stratification of the study area into a coastal, a mountainous and an interior stratum proved to be successful, reducing the Mean Squared Error of Prediction with up to 55%.     

Deglaciation chronology inferred from marine sediments in a proglacial lake basin, western Spitsbergen, Svalbard

Sub-bottom sediment profiles and sediment cores show that the lacustrine sediments in lake Linnevatnet are underlain by marine sediments and a basal till that mantles the bedrock. The till was probably deposited by the glacier that during the Late Weichselian glacial maximum removed all pre-existing sediments from the basin. The cores were collected in closed basins, where continuous deposition is expected. The marine sediment in the studied cores is up to 8 m thick and consists of bioturbated clay and silt. Radiocarbon dates on shells from the base of the marine sequence suggest that glacial retreat from the lake basin occurred around 12,500BP. This is more than a thousand years older than basal shell dates from raised marine sediments on the slopes above the lake. Typical ice proximal litbofacies were not identified in the cores. stratigraphic record indicates both a rapid glacial retreat and that no younger glacial re-advances occurred. During the Younger Dryas local glaciers on western Svalbard were smaller than during the Little Ice Age. This is in sharp contrast to western Europe, where Younger Dryas glaciers were much larger than those the Little Ice Age.     

Fully nonlinear Boussinesq equations for long wave propagation and run-up in sloping channels with parabolic cross sections

A general framework for derivation of long wave equations in narrow channels, and their transformation to Lagrangian coordinates is briefly established. Then, fully nonlinear Boussinesq equations are derived for channels of parabolic cross sections. The simplified version with normal nonlinearity is compared with corresponding models from the literature, and propagation properties are discussed. A Lagrangian run-up model is adapted to the fully nonlinear set. This model is tested by means of controlled residues and by a well-controlled comparison to exact analytic solutions from the literature. Then, run-up of solitary waves in simple geometries is simulated and compared to a semi-analytic solution that is derived for propagation and run-up in a composite channel. The dispersive model retains the higher run-up height in a parabolic channels, as reported in the recent literature for NLSW solutions, as compared to a rectangular channel.     

Short-term Jovian rotation profiles, 1970–1972

Approximately 1300 measurements of the positions of 101 features in Jupiter's atmosphere have been made using blue-light photographs of the planet obtained by the International Planetary Patrol from 1970 to 1972. The longitudinal positions of features were read directly with orthographic grids superimposed on optically projected images of Jupiter. For each feature, least-squares linear fits were made on plots of the longitude measurements as a function of time, in order to derive drifts rates relative to System I or II. Drift rates were used to compute rotation periods; and, by combining the data from various latitudes, short-term rotation profiles were constructed. These short-term profiles are compared with a “mean” multiple-year profile, and differences in detail are evident. Slightly shorter rotation periods were found near the edges of the equatorial jet than at its center in 1970 and 1971. In 1972, one feature at +37° north was found to exhibit an abrupt change in period amounting to an increase of 95.1 seconds.     

Untersuchungen der Himmelsstrahlung in den Ostalpen mit besonderer Berücksichtigung ihrer Höhenabhängigkeit

Zusammenfassung Als Beitrag zur Kenntnis der verschiedenen Faktoren der Strahlungsbilanz wird in dieser Studie im besonderen die Verteilung der Himmelsstrahlung mit der Seehöhe behandelt.Bei wolkenlosem Himmel zeigt sich, entsprechend der geringeren Zerstreuung in größeren Seehöhen, eine Abnahme der Himmelsstrahlung. Eine beachtliche Störung der reinen Höhenabhängigkeit bilden multiple Reflexion und Reflexion der direkten Sonnenstrahlung durch horizontüberhöhende Hänge.Eine Sonderstellung nimmt die Himmelsstrahlung in Städten ein. Entsprechend dem Gang der Lufttrübung erscheint das Maximum im Tagesgang gegen den Vormittag verschoben.Bei völlig bedecktem Himmel zeigt sich ein starker Intensitätsanstieg der Himmelsstrahlung mit zunehmender Seehöhe. Es steigt z. B. die Intensität der Himmelsstrahlung auf dem Sonnblick (3106 m) auf 200% des Wertes von Wien (202 m) im Sommer und auf 400% im Winter. Sowohl für klaren, als auch für bedeckten Himmel werden Richtwerte der Himmelsstrahlung für verschiedene Seehöhen in 500 m-Intervallen angegeben.Aufbauend auf die beiden vorangehenden Kapitel wird im letzten versucht, eine Höhenabhängigkeit für wechselnden Bewölkungsgrad zu finden.

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Summary This study dealing particularly with the radiation of the sky as a function of altitude is a contribution to what we know about the different factors of radiation balance. In the absence of clouds the radiation of the sky shows a decrease with height according to less light being scattered at greater altitudes. This dependence on height is considerably disturbed by multiple reflection and reflection of direct solar radiation by slopes rising above the horizon. Sky radiation has a particular character in great towns. In relation to the variations of air turbidity there is a shift of its daily maximum towards forenoon. Intensity of sky radiation increases strongly with altitude in case of an entirely overcast sky. Intensity values of sky radiation on the Sonnblick (3106 m) reach e. g. 200 per cent of the values observed in Vienna (202 m) in summer and 400 per cent in winter. Approximate values of sky radiation in different altitudes with intervals of 500 m are given for clear and overcast sky. An attempt has been made, in the last chapter, to find a dependence on height for different degrees of cloudiness.

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Résumé Considérée comme contribution à la connaissance des différents facteurs du bilan radiatif, la présente étude traite en particulier de la répartition du rayonnement céleste en fonction de l'altitude. Par ciel serein le rayonnement céleste diminue avec l'altitude par suite de l'affaiblissement de la dispersion. La loi de décroissance est toutefois altérée par la réflexion multiple et par celle du rayonnement solaire direct sur les versants dépassant l'horizon. Le rayonnement céleste dans les villes constitue un cas spécial. La variation du trouble atmosphérique entraine un déplacement du maximum vers le matin. Par ciel entièrement couvert l'intensité du rayonnement céleste éprouve une forte augmentation avec l'altitude; cette intensité atteint par exemple au Sonnblick (3106 m) 200% de cell Vienne (202 m) en été, et 400% en hiver. On donne des valeurs types du rayonnement céleste pour différentes altitudes de 500 en 500 m, aussi bien par ciel serein que couvert. On tente enfin d'établir la loi de variation du rayonnement céleste avec l'altitude pour différentes fractions de couverture nuageuse du ciel.

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Mit 17 Textabbildungen.     

Untersuchungen über die Strahlungsverhältnisse auf den Alpengletschern

Zusammenfassung Auf dem Hohen Sonnblick (3106 m) wurden im Sommer 1950 Wärmeumsatzuntersuchungen durchgeführt. Über die hierbei ausgeführten Messungen der Sonnenstrahlung, Himmelsstrahlung, Gegenstrahlung der Atmosphäre, der Albedo und der langwelligen Temperaturausstrahlung des Gletschers wird hier berichtet. Es konnte die Einwirkung der Bewölkung auf die Himmelsstrahlung studiert werden. Bestimmungen der Gegenstrahlung über Bilanzmessungen ergaben die Brauchbarkeit derÅngströmschen Formel und bestimmte Gesetzmäßigkeiten des Einflusses der Wolkendecke. Als anscheinend variabelster Faktor wird die zeitlich und örtlich oft sehr wechselnde Albedo angesehen. Einige Beispiele direkter Strahlungsbilanzmessungen, die dies beweisen, werden mitgeteilt.

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Summary A report is given of measurements of solar radiation, sky radiation, atmospheric radiation, albedo, and long-wave outgoing radiation of a glacier carried out in connection with investigations on exchange of heat on the High Sonnblick (3106 m) in summer 1950. The effects of cloudiness on sky radiation were studied. Determinations of atmospheric radiation derived from balance measurements showed the validity of theÅngström-formula and certain regularities concerning the effect of cloud cover. The most variable factor appears to be the albedo which often varies strongly with time as well as locally. Several examples of direct measurements of radiation balance proving that are communicated.

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Résumé On a effectué au sommet du Sonnblick (3106 m) en été 1950 des recherches sur les échanges de chaleur. On rapporte ici sur les mesures faites du rayonnement solaire et céleste, du rayonnement atmosphérique de l'albédo et du rayonnement à grande longueur d'onde du glacier. On a pu établir l'influence de la nébulosité sur le rayonnement céleste. Des évaluations du rayonnement atmosphérique tirées de mesures du bilan thermique ont prouvé la validité de la formule d'Ångström ainsi que certaines règles concernant l'effet de la couverture du ciel. Le facteur apparemment le plus variable est l'albédo qui varie parfois fortement dans le temps et dans l'espace. Quelques exemples de mesures directes du bilan radiatif qui le prouvent sont donnés.

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Mit 6 Textabbildungen.     

Effect of Moisture on Attraction Force in Beach Sand

Beach sands located above the sea water level exist in an unsaturated, rather than a fully saturated or dry state. Within the unsaturated zone, a steep excavated surface can be sustained for some unknown but finite time, and some slopes may remain stable for extended time periods due to capillary forces. These observations clearly indicate small but nonzero values for attraction strength (tensile strength and cohesion) in unsaturated beach sands, especially apparent but not confined to settings where there are low stress levels. Thus, experiments were carried out to quantify the magnitude of attraction strength in moist sands (D_r = 30%) and to examine the variation of these values as a function of moisture content and presence of a small amount of fines. Tensile strength, which is significantly different from zero, increases with increasing moisture content and fines. However, the influences of fines on the tensile strength are substantially dependent on the water content. Apparent cohesion strength is also identified in moist sands. A simple relationship between tensile strength and apparent cohesion is proposed using the obtained data. This study would help to further understand the phenomenon of stability of beach sands.     

Reference points for optimal fish stock management: A lesson to be learned from the Northeast Arctic cod stock

In the North Atlantic the Icelandic, the North Sea, and the Newfoundland cod stocks are currently overexploited. Overexploitation also characterised the Northeast Arctic cod stock, but effective management measures introduced in 1990 and the years thereafter have brought this stock within safe biological limits. The Northeast Arctic cod stock is transboundary and shared between Norway and Russia. As guidelines for a sound management strategy of this cod stock in the future, reference points for management are discussed. As a point of departure, a management strategy which fulfils the objectives for fishery policy stated by Norway is analysed. These objectives, focusing on sustainable harvesting, increased profitability and the role of the fishery as employer of labour in rural districts are fundamental in most of the world's fishery nations.The “optimal” strategy is defined as the one which fulfils these in the best way possible. The natural variations are discussed and the biological and economic yield's dependence upon the rate of exploitation are analysed. The analysis shows that the size of the spawning stock should be no less than 500 000 tonnes and that highest yield is obtained through a rate of exploitation of around 17–30% (equivalent to a fishing mortality of about 0.20–0.40). A spawning stock size of 500 000 tonnes should therefore serve as a “limit reference point” and a fishing mortality of about 0.20–0.40 should serve as a “target reference point” in the management of Northeast Arctic cod.The method described may be applied to other demersal stocks to help establish target and limit reference points in order to conduct a sound management.