Stochastic aspects in combined Doppler and triangulation nets

Summary The “true” geocentric position of any terrestrial triangulation can be reached to a certain degree of approximation only. Every claimed “geocentric” terrestrial system, therefore, must be capable of undergoing some minor shifts and minor rotations. In a two dimensional solution which provides the best combination of the two systems in question, three degrees of freedom are open and must be filled by corresponding statements or conditions. But the parameters so obtained are of relative value only. Thus, every two-dimensional solution must be followed by a three-dimensional solution in order to obtain the best external parameters and the best internal consistency. This sequential processing is legitimate because an alteration of the values of the external parameters no longer changes the inner shape of the combined network. All decisions made about the model have the character of hypotheses and must be tested statistically.     

A Mathematical View of Weights-of-Evidence,Conditional Independence,and Logistic Regression in Terms of Markov Random Fields

New light is shed on mathematical methods of potential modeling from the point of view of Markov random fields. In particular, weights-of-evidence and logistic regression models are discussed in terms of graphical models possessing Markov properties, where the notion of conditional independence is essential, and will be related to log-linear models. While weights-of-evidence with respect to indicator predictor variables and logistic regression with unrestricted predictor variables model conditional probabilities of an indicator random target variable, the subject of log-linear models is the joint probability of random variables. The relationship to log-linear models leads to a likelihood ratio test of conditional independence, rendering an omnibus test of conditional independence restricted by a normality assumption obsolete. Moreover, it reveals a hierarchy of methods comprising weights-of-evidence, logistic regression without interaction terms, and logistic regression including interaction terms, where each former method is a special case of the consecutive latter method. The assumptions of conditional independence of all predictor variables given the target variable lead to logistic regression without interaction terms. Violations of conditional independence are compensated exactly by corresponding interaction terms, no cumbersome approximate corrections are needed. Thus, including interaction terms into logistic regression models is an appropriate means to account for lacking conditional independence. Logistic regression exempts from the burden to worry about lack of conditional independence. Eventually, the relationship to log-linear models renders logistic regression with indicator predictor variables optimum for discrete predictor variables. Weights-of-evidence applies for indicator predictor variables only, logistic regression applies without restrictions of the type of predictor variables and approximates the proper distribution in the general case.     

Intra‐event scale bar–bank interactions and their role in channel widening

Channel bars and banks strongly affect the morphology of both braided and meandering rivers. Accordingly, bar formation and bank erosion processes have been greatly explored. There is, however, a lack of investigations addressing the interactions between bed and bank morphodynamics, especially over short timescales. One major implication of this gap is that the processes leading to the repeated accretion of mid‐channel bars and associated widenings remain unsolved. In a restored section of the Drau River, a gravel‐bed river in Austria, mid‐channel bars have developed in a widening channel. During mean flow conditions, the bars divert the flow towards the banks. One channel section exhibited both an actively retreating bank and an expanding mid‐channel bar, and was selected to investigate the morphodynamic processes involved in bar accretion and channel widening at the intra‐event timescale. We repeatedly surveyed riverbed and riverbank topography, monitored riverbank hydrology and mounted a time‐lapse camera for continuous observation of riverbank erosion processes during four flow events. The mid‐channel bar was shown to accrete when it was submerged during flood events, which at the subsequent flow diversion during lower discharges narrowed the branch along the bank and increased the water surface elevation upstream from the riffle, which constituted the inlet into the branch. These changes of bed topography accelerated the flow along the bank and triggered bank failures up to 20 days after the flood events. Four analysed flow events exhibited a total bar expansion from initially 126 m² to 295 m², while bank retreat was 6 m at the apex of the branch. The results revealed the forcing role of bar accretion in channel widening and highlighted the importance of intra‐event scale bed morphodynamics for bank erosion, which were summarized in a conceptual model of the observed bar–bank interactions. Copyright © 2015 John Wiley & Sons, Ltd.     

Insights into Holocene relative sea-level changes in the southern North Sea using an improved microfauna-based transfer function

In light of global warming and rising relative sea level (RSL), detailed reconstructions of RSL histories and their controlling processes are essential in order to manage coastal-protection challenges. This study contributes to unravelling Holocene RSL change on the East Frisian North Sea coast in high resolution and with a new approach for the German Bight. For the first time, a transfer function (vertical error: 29.7 cm ? ~11% of the mean tidal range) for RSL change based on a combined training set of benthic foraminifers and ostracods from the back-barrier tidal basin of Spiekeroog is applied to the Holocene record of the back-barrier tidal basin of Norderney. The resulting RSL curve for the Norderney tidal basin is corrected for decompaction and shows a deceleration in RSL rise between 6000 and 5000 cal bp. The smallest possible error envelope (~1 m) results from the good suitability of salt-marsh layers between 5000 and 4000 cal bp. The RSL curve provides an approach towards the closure of the common data gap of peat-based curves for the southern North Sea related to a lack of basal peats in the youngest age range, and verifies regional differences in glacial isostatic adjustment.