Expectation Maximization algorithm and its minimal detectable outliers

Minimal Detectable Biases (MDBs) or Minimal Detectable Outliers for the Expectation Maximization (EM) algorithm based on the variance-inflation and the mean-shift model are determined for an example. A Monte Carlo method is applied with no outlier and with one, two and three randomly chosen outliers. The outliers introduced are recovered and the corresponding MDBs are almost independent from the number of outliers. The results are compared to the MDB derived earlier by the author. This MDB approximately agrees with the MDB for one outlier of the EM algorithm. The MDBs for two and three outliers are considerably larger than MDBs of the EM algorithm.     

The Wadden Sea in transition - consequences of sea level rise

The impact of sea level rise (SLR) on the future morphological development of the Wadden Sea (North Sea) is investigated by means of extensive process-resolving numerical simulations. A new sediment and morphodynamic module was implemented in the well-established 3D circulation model GETM. A number of different validations are presented, ranging from an idealized 1D channel over a semi-idealized 2D Wadden Sea basin to a fully coupled realistic 40-year hindcast without morphological amplification of the Sylt-Rømøbight, a semi-enclosed subsystem of the Wadden Sea. Based on the results of the hindcast, four distinct future scenarios covering the period 2010–2100 are simulated. While these scenarios differ in the strength of SLR and wind forcing, they also account for an expected increase of tidal range over the coming century. The results of the future projections indicate a transition from a tidal-flat-dominated system toward a lagoon-like system, in which large fractions of the Sylt-Rømøbight will remain permanently covered by water. This has potentially dramatic implications for the unique ecosystem of the Wadden Sea. Although the simulations also predict an increased accumulation of sediment in the back-barrier basin, this accumulation is far too weak to compensate for the rise in mean sea level.     

Insights into agricultural influences and weathering processes from major ion patterns

Karst areas and their catchments pose a great challenge for protection because fast conduit flow results in low natural attenuation of anthropogenic contaminants. Studies of the hydrochemistry of karst sources and river solutes are an important tool for securing and managing water resources. A study of the geochemical downriver evolution of the Wiesent River and its tributaries, located in a typical karst terrain, revealed unexpected downstream decreases of nitrate with maximum mean values of 30 mg/L at the source to minimum values of 18 mg/L near the river mouth. This trend persisted over the length of the river even though increased agricultural activities are evident in the downstream section of the catchment. This pattern is caused by fertilizer inputs via diffusive and fast conduits flow from karst lithology in the upstream area that may have reached the river's source even from beyond the hydrological catchment boundaries. Further downstream, these influences became diluted by tributary inputs that drain subcatchments dominated by claystone and sandstone lithologies that increased potassium and sulphate concentrations. Our findings indicate that bedrock geology remains the dominant control on the major ion chemistry of the Wiesent River and that agricultural influences are strongest near the headwaters despite increased land use further downstream, due to long‐term storage and accumulation in karst aquifers. This feature may not be unique to the Wiesent River system, as carbonates cover significant portions of the Earth's surface and subsequent work in other river systems could establish whether such patterns are ubiquitous worldwide.     

BARENTS16: a 1-D velocity model for the western Barents Sea

A minimum 1-D seismic velocity model for routine seismic event location purposes was determined for the area of the western Barents Sea, using a modified version of the VELEST code. The resulting model, BARENTS16, and corresponding station corrections were produced using data from stations at regional distances, the vast majority located in the periphery of the recorded seismic activity, due to the unfavorable land–sea distribution. Recorded seismicity is approached through the listings of a joint bulletin, resulting from the merging of several international and regional bulletins for the region, as well as additional parametric data from temporary deployments. We discuss the challenges posed by this extreme network-seismicity geometry in terms of velocity estimation resolution and result stability. Although the conditions do not facilitate the estimation of meaningful station corrections at the farthermost stations, and even well-resolved corrections do not have a convincing contribution, we show that the process can still converge to a stable velocity average for the crust and upper mantle, in good agreement with a priori information about the regional structure and geology, which reduces adequately errors in event location estimates.     

Carry-over effects of the membrane interface probe

The membrane interface probe (MIP) is widely used to characterize the subsurface distribution of volatile organic compounds (VOCs). One problem that arises during MIP application is that disproportionately high MIP signals are obtained after passing source zones which contain mobile or residual phases. This serious problem occurs because of a carry-over effect, in particular caused by compound-specific retention times in the conventional unheated transfer line, commonly used during such an investigation. The objective of this study was to perform a qualitative methodical field evaluation of the carry-over effect of a conventional MIP system with a conventional unheated transfer line. This was achieved by coupling a mobile mass spectrometer to the MIP device. Results obtained were then further compared with those achieved using a laser induced fluorescence (LIF) system. Because of this coupling, time- and depth-dependent signals for different substances became known. Field evaluation data obtained showed complex superpositions of compounds with MIP system results. As a result of this superposition, MIP signals from the saturated zone beneath the source zone (zone with free and/or residual phase) are blurred and are therefore not representative of particular depths. However, utilizing multidirectional probing alongside conventional MIP probing (forwards and backwards), it was possible to detect the upper and lower phase boundary of the source zone. These MIP results correlated excellently with the LIF results. An important conclusion that can be drawn from the field investigation is that coupling a mobile mass spectrometer to the MIP system enables advanced MIP signal interpretation to be successfully achieved.     

A dynamo model with double diffusive convection for Mercury's core

A recent dynamo model for Mercury assumes that the upper part of the planet's fluid core is thermally stably stratified because the temperature gradient at the core–mantle boundary is subadiabatic. Vigorous convection driven by a superadiabatic temperature gradient at the boundary of a growing solid inner core and by the associated release of light constituents takes place in a deep sub-layer and powers a dynamo. These models have been successful at explaining the observed weak global magnetic field at Mercury's surface. They have been based on the concept of codensity, which combines thermal and compositional sources of buoyancy into a single variable by assuming the same diffusivity for both components. Actual diffusivities in planetary cores differ by a large factor. To overcome the limitation of the codensity model, we solve two separate transport equations with different diffusivities in a double diffusive dynamo model for Mercury. When temperature and composition contribute comparable amounts to the buoyancy force, we find significant differences to the codensity model. In the double diffusive case convection penetrates the upper layer with a net stable density stratification in the form of finger convection. Compared to the codensity model, this enhances the poloidal magnetic field in the nominally stable layer and outside the core, where it becomes too strong compared to observation. Intense azimuthal flow in the stable layer generates a strong axisymmetric toroidal field. We find in double diffusive models a surface magnetic field of the observed strength when compositional buoyancy plays an inferior role for driving the dynamo, which is the case when the sulphur concentration in Mercury's core is only a fraction of a percent.     

Reconstruction of groundwater levels to impute missing values using singular and multichannel spectrum analysis: application to the Ardabil Plain,Iran

ABSTRACT

Groundwater-level time series often have a substantial number of missing values which should be taken into consideration before using them for further analysis, particularly for numerical groundwater flow modelling applications. This study aims to comprehensively compare two data-driven models, singular spectrum analysis (SSA) and multichannel spectrum analysis (MSSA), to reconstruct groundwater-level time series and impute the missing values for 25 piezometric stations in Ardabil Plain, northwest Iran. The reconstructed groundwater-level time series are assessed against the complete observed groundwater time series, while the imputed values are appraised against the artificially created gap values. The results show that both SSA and MSSA demonstrate a solid competency in imputation and reconstruction of groundwater-level data. However, depending on the spatial correlation between the piezometers, and the most suitable probability distribution function (pdf) fitted to the time series of each piezometer, the performance may vary from piezometer to piezometer.     

Zur Erfassung und Statistik der kleinsten Niederschläge

Zusammenfassung H?ufigkeitsverteilungen nach logarithmischen Merkmalsskalen er?ffnen für die Niederschlagsstatistik das bisher nicht bekannte Gebiet kleinster Niederschlagsmengen unter 0.05 mm, dessen Erfassung nach Tropfenbildregistrierungen m?glich wird. Nahezu die H?lfte aller Einzelniederschl?ge fallen in diesen Bereich. Das H?ufigkeitsmaximum der Tages- und Terminsummen von einigen mm rückt bei den Einzelniederschl?gen in den Bereich von 0.03 bis 0.04 mm. Der Erfassung der kleinsten Niederschl?ge kommt neben einer praktischen (Pflanzenphysiologie, Sch?dlingsbiologie) auch eine theoretische Bedeutung zu.

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Summary The use of logarithmic scales in statistical precipitation research introduces in the unknown range of diminutive and minute amounts of precipitation less than 0.05 mm, the catch of which is possible by raindrop recordings. Nearly half of single rainfalls belongs to this class. Regarding to daily sums the maximum in frequency distribution amounts a range of some mm. In single rainfalls the maximal range shifts to 0.03–0.04 mm. The investigation of minute precipitation amounts is important with regard to practical and theoretical use.

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Dipl. Ing. Dr.Johannes Grunow, Meteorologisches ObservatoriumHohenpeissenberg (Oberbayern).