Integral formulas for heterogeneous data in physical geodesy

The least squares estimator is derived for a random stochastic process implied by one or two heterogeneous random stochastic processes on a sphere. The solution can be regarded as least squares collocation in the continuous case. When the method is applied in physical geodesy the statistical expectation is usually substituted by the global average and the method will then give the minimum mean squares errors of the estimated quantities. The solutions can also be considered as generalizations of the classical integral formulas in physical geodesy for heterogeneous data information.     

Triassic lacustrine red-beds and palaeoclimate: The „Buntsandstein“ of Helgoland and the malmros Klint member of East Greenland

The playa-lake origin of the Lower Triassic Buntsandstein of Helgoland and the Upper Triassic Malmros Klint Member of East Greenland is suggested by: the continental setting; absence of marine fossils and occurrence of fresh-water trace fossils; evidence of shallow water, fluctuations in water level, frequent subaerial exposure and oxidizing depositional conditions; evidence of low-energy wave-action and absence of evidence for tidal influence. The Buntsandstein contains aeolian dunes and evaporites, but only rare fluvial sandstones and very rare fresh-water trace fossils. In contrast the Malmros Klint Member contains no aeolian sandstones and evaporites, but common fluvial sandstones and numerous fresh-water trace fossils. Wave ripple crest orientation suggests that both sequences were deposited during the influence of alternating NE and SE trade winds. The Buntsandstein appears to have been deposited in a central trade wind region with dominant winds from SE and short rainy seasons; the Malmros Klint Member was apparently deposited in a marginal trade wind region with dominant NE winds and longer rainy seasons.

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Zusammenfassung Der Buntsandstein auf Helgoland und der Malmros Klint Member (Obere Trias) in Ostgrönland werden als Playaseebildungen interpretiert auf Grund von: Vorkommen von Süßwasser-Lebenspuren und Mangel an marinen Fossilien; Beweise für Seichtwasser, Schwankungen in Wassertiefen, häufige Trockenlegung und oxydierende Ablagerungsverhältnisse; Beweise für schwachen Wellenschlag aber Mangel an Gezeiten; der stratigraphischen Einfügung in einer kontinentalen Schichtenfolge. Der Buntsandstein enthält Winddünen und Evaporite, aber nur wenige fluviatile Sandsteine und einzelne Süßwasser-Lebenspuren. Im Gegensatz dazu enthält der Malmros Klint Member keine äolische Sandsteine und keine Evaporite, sondern viele fluviatile Sandsteine und zahlreiche Süßwasser-Lebenspuren. Die Orientierung der Oszillationsrippelkämme beweist vermutlich, daß die beiden Schichtenfolgen während des Einflusses umlaufender Nordost- und Südostpassatwinde abgelagert wurden. Der Buntsandstein wurde wahrscheinlich in einer zentralen Passatwindregion mit vorherrschenden Südostwinden und kurzen Regenperioden abgelagert; der Malmros Klint Member wurde wahrscheinlich in einer Randpassatwindregion mit vorherrschenden Nordostwinden und längeren Regenperioden abgelagert.

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Résumé Le Grès bigarré (Trias inférieur) de Héligoland et le Malmros Klint Member (Trias supérieur) du Groenland oriental sont interprétés comme des formations lacustres éphémères à cause de: présence d'ichnofossiles d'eau douce et l'absence de fossiles marins; évidence d'eau peu profonde, variation de la profondeur d'eau fréquentes dessiccations et conditions sédimentaires oxydantes; évidence d'action calme des vagues, mais absence de marée; 1'emplacement stratigraphique dans une séquence continentale. Le Grès bigarré contient des dépôts éoliens et des évaporites, mais peu de grès fluviatiles et des ichnofossiles rares d'eau douce. Par contre le Malmos Klint Member ne contient ni de grès éoliens, ni d'évaporites, mais plusieurs grès fluviatiles et de nombreux ichnofossiles d'eau douce. L'orientation des crêtes ripplemarks semble prouver que les deux séquences ont été déposées sous l'influence des alizés du nord-est et du sud-est. Le Grès bigarré de Héligoland semble s'être déposé dans une région centrale des alizés avec des vents dominants du sud-est et de brèves saisons pluvieuses. Evidemment le Malmros Klint Member s'est déposé dans une région marginale des alizés avec des vents dominants du nord-est et des saisons pluvieuses plus longues.

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The length of closed geomorphic lines

This paper is based on the study of shore line length of 12 Swedish lakes on various maps ranging in scale from 1:10,000 1:1,000,000. The lakes differ in size, from Lake Munksjön, which has an area of 1.1 km², to Lake Vänern with an area of 5893 km², and also in shore line irregularity, ranging from the rather regular basins of Lake Munksjön and Lake Erken to the very irregular basin of Lake Mälaren. A “new ” method, the checkered transparent paper method (the CTP-method), was adopted to measure the shore length of certain lakes on various maps. Length determination by this method can be executed quickly and easily, and in a statistically definable way, giving comparable data from various types of map. A formula defining the functional relationship between scale, shore irregularity, shore length, and lake area has been derived: $$NF = F(K_{2} - K_{1})/[K_{2} - log(s + a)]$$ or $$1_{n} = 1(K_{2} - K_{1} )/[K_{2} - log(s + a)]$$ where NF = the normalized shore development (shore irregularity) at a scale of 1:1; F = the shore development as determined on a given map scale; s = the scale factor (10,000, 50,000 etc); a = 10⁵ ? log A, where 10⁵ = the area constant; A = the lake area in km²; K₁ = log(s + a) for s = 1, i.e. the reference scale; K₂ = log(s + a) for s = 6,000,000, where 6,000,000 is called the scale constant; 1 = the shore length as determined by the CTP-method on a given map; and 1_n = the normalized shore length at a scale of 1:1. The formula offers a high degree of accuracy and the length of any closed geomorphic line can be determined independently of map scale, under given practical limitations. The length value obtain is the normalized length, that is the best approximation of the real, natural length at a scale of 1:1.     

Exploring socio-hydrological determinants of crop yield in under-performing irrigation schemes: pathways for sustainable intensification

ABSTRACT

Understanding the human–water–food–climate nexus is central to achieving sustainable intensification (SI) in agriculture. This research uses a socio-hydrological approach to understand the underpinning for implementing SI in the Gezira Irrigation Scheme, Sudan, by integrating vegetation indices derived from remote sensing, ancillary, gridded soil and precipitation data, supplemented by interviews with 393 farmers. The productivity gap was estimated as the difference between the potential and actual productivities. Based upon data on farmers’ socio-economic status and field practices, a regression tree model was built to determine the factors that control the sorghum yield. The model revealed that the financial status of farmers and access to water are the most influential factors on sorghum yield. A conceptual framework that elucidates SI and its bi-directional feedback to the environment, society and the economy is proposed. Implementing SI in the scheme has implications on water and food security in Sudan and beyond its borders.     

The establishment of a GPS deformation network in the ethiopian rift valley

In April and May 1989 the satellite Global Positioning System (GPS) was employed in the establishment of three deformation networks in the Ethiopian Rift Valley. The net E1 consists of 6 points of about 100–270 km interdistances, with two points located on each of the African and the Somalian plate and two points down in the rift. In addition two separate GPS traverses were established: one (E2) runs across the rift, and one (E3) runs about 500 km along the rift.The remeasurement of a 175 km long baseline included in two subcampaigns indicates a repeatability of the GPS observations of the order of 1×10⁻⁷ and 3×10⁻⁷ for slope distance and ellipsoidal height, respectively.Along the E2 traverse GPS/trigonometric levelled geoid undulations and gravimetric geoid undulations agree well, while the discrepancy along the E3 traverse needs further analysis.     

A simple method of quantifying filamentous algae in microscope

A fast and simple method to quantify filamentous algae in inverted microscope is described. It is based on the number of intersections between the midline of a diametrical transect and the filaments on the chamber bottom. It is shown to be theoretically sound and is compared with the common length measurement method.     

A double layer review

A review is given of the main results on electrostatic double layers (sometimes called space charge layers or sheaths) obtained from theory and laboratory and space experiments up to the spring of 1977.The paper begins with a definition of double layers in terms of potential drop, electric field, and charge separation. Then a review is made of the theoretical results obtained so far. This covers, among other things, necessary criteria for existence and stability, quantitative estimates of charge separation and thickness, and some probable cause of DL-formation in terms of an instability.Next, experimental results obtained in the laboratory are compared with the theoretical results. Due to recent progress in experimental technique, the interior of a double layer can now be studied in much more detail than was possible before.By means of barium jets and satellite probes, double layers have now been found at the altitudes that were previously predicted theoretically. The general potential distribution above the auroral zone, suggested by inverted V-events and electric field reversals, is corroborated.Paper dedicated to Professor Hannes Alfvén on the occasion of his 70th birthday, 30 May, 1978.     

Characterization and induction of cytochrome P-450 in the rainbow trout kidney

Cytochrome P-450 monooxygenases catalyze the biotransformation of a great variety of foreign, as well as endogenous, lipid-soluble compounds to more water-soluble products. As in mammals, highest concentration of cytochrome P-450 in fish is found in the liver. However, previous studies have indicated that fish kidney contains relatively high cytochrome P-450-mediated activities.^1,2 We have therefore prepared and characterized subcellular fractions from the kidney of rainbow trout suitable for studies on cytochrome P-450-dependent reactions. Furthermore, as in the liver, several cytochrome P-450-mediated reactions in the kidney were induced following treatment of the fish with β-naphthoflavone.