Multicollinearity and correlation among local regression coefficients in geographically weighted regression

Present methodological research on geographically weighted regression (GWR) focuses primarily on extensions of the basic GWR model, while ignoring well-established diagnostics tests commonly used in standard global regression analysis. This paper investigates multicollinearity issues surrounding the local GWR coefficients at a single location and the overall correlation between GWR coefficients associated with two different exogenous variables. Results indicate that the local regression coefficients are potentially collinear even if the underlying exogenous variables in the data generating process are uncorrelated. Based on these findings, applied GWR research should practice caution in substantively interpreting the spatial patterns of local GWR coefficients. An empirical disease-mapping example is used to motivate the GWR multicollinearity problem. Controlled experiments are performed to systematically explore coefficient dependency issues in GWR. These experiments specify global models that use eigenvectors from a spatial link matrix as exogenous variables.This study was supported by grant number 1 R1 CA95982-01, Geographic-Based Research in Cancer Control and Epidermiology, from the National Cancer Institute. The author thank the anonymous reviewers and the editor for their helpful comments.     

Structural elements in southeastern Quebec,northwestern Appalachians,Canada

An attempt is made to correlate and separate in terms of style and time two contrasting sets of structural elements in the northwestern part of the Appalachian Uplands in the Province of Quebec, Canada. There is sufficient evidence to indicate that a fold system with north-south trending axes is superimposed on a fold system with east-west axes. It is suggested that the two sets of structures represent pulses of one long-continued deformation accompanied by corresponding early and late phases of metamorphism.

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Zusammenfassung Es wurde versucht, in den Appalachen des südöstlichen Teiles der Provinz Quebec, Kanada, zwei ungleichzeitige tektonische Systeme verschiedenen Baustils zu trennen. Die komplexen Kleinstrukturen zeigen, da\ Ost-West streichende Faltenachsen von einer jüngeren Nord-Süd-Faltung überprägt worden sind. Der Autor ist der Meinung, da\ die zwei tektonischen Systeme, die von einer frühen und späten Phase der Metamorphose begleitet werden, den zeitlich getrennten Verformungsstadien einer Orogenese entsprechen.

     

The role of prior model calibration on predictions with ensemble Kalman filter

This paper, based on a real world case study (Limmat aquifer, Switzerland), compares inverse groundwater flow models calibrated with specified numbers of monitoring head locations. These models are updated in real time with the ensemble Kalman filter (EnKF) and the prediction improvement is assessed in relation to the amount of monitoring locations used for calibration and updating. The prediction errors of the models calibrated in transient state are smaller if the amount of monitoring locations used for the calibration is larger. For highly dynamic groundwater flow systems a transient calibration is recommended as a model calibrated in steady state can lead to worse results than a noncalibrated model with a well-chosen uniform conductivity. The model predictions can be improved further with the assimilation of new measurement data from on-line sensors with the EnKF. Within all the studied models the reduction of 1-day hydraulic head prediction error (in terms of mean absolute error [MAE]) with EnKF lies between 31% (assimilation of head data from 5 locations) and 72% (assimilation of head data from 85 locations). The largest prediction improvements are expected for models that were calibrated with only a limited amount of historical information. It is worthwhile to update the model even with few monitoring locations as it seems that the error reduction with EnKF decreases exponentially with the amount of monitoring locations used. These results prove the feasibility of data assimilation with EnKF also for a real world case and show that improved predictions of groundwater levels can be obtained.     

Bildung bromhaltiger Desinfektionsnebenprodukte nach Chlorung von Bodenseewasser in Abhängigkeit von Aufbereitungsschritten und der Bromidkonzentration

Formation of Brominated Disinfection By-products after Chlorination of Water from Lake Constance Depending on Treatment Steps and Bromide Concentration The formation of halogenated disinfection by-products (DNP) (trihalomethanes (THM), haloacetic acids (HES), haloacetonitriles (HAN), haloketones (HKE) and chloropicrin (TCNM)) was studied after chlorination (0.5 mg/L) of raw water and drinking water from Lake Constance. The objectives of this study were to investigate the effect of bromide ion on the distribution of DNP-species resulting from chlorination and to draw up a bromide mass-balance. The treatment of water from Lake Constance with ozone decreased the formation of DNP about 35% and of total organic halogens (AOX) about 45%. This decline in DNP-formation is mainly due to the formation of chloroform, dichloro- and trichloroacetic acid. Though there is only a small amount of bromide (6.2 μg/L) in water from Lake Constance, about 32% of THM, 16% of HES, and 30% of HAN contained bromine after chlorination of treated water. The addition of bromide ion (up to 1 mg/L) shifted the DNP-composition to more brominated species. The distribution of the DNP-species depends on the initial molar bromide-to-chlorine ratio. A mathematic model showed the same pattern of DNP-species depending on the initial molar bromide-to-chlorine ratio that was observed experimentally in microstrained raw water and drinking water from Lake Constance. After chlorination of microstrained raw water, 27% of the bromide were incorporated in known DNP, 34% in unknown substances, and about 39% of bromide were not converted to organic bromine. After chlorination of treated water, only 16% of the bromide were incorporated in unknown substances, whereas 34% were found in known DNP. About 50% were found as bromide again. After addition of bromide (up to 25 μg/L) to ozonated and treated water from Lake Constance, between 60 and 72% of the bromide that had reacted after chlorination were found in analyzed low-molecular DNP.     

Developing a modern pollen–climate calibration data set for Norway

Bjune, A. E., Birks, H. J. B., Peglar, S. M. & Odland, A. 2010: Developing a modern pollen–climate calibration data set for Norway. Boreas, Vol. 39, pp. 674–688. 10.1111/j.1502‐3885.2010.00158.x. ISSN 0300‐9483. Modern pollen–climate data sets consisting of modern pollen assemblages and modern climate data (mean July temperature and mean annual precipitation) have been developed for Norway based on 191 lakes and 321 lakes. The original 191‐lake data set was designed to optimize the distribution of the lakes sampled along the mean July temperature gradient, thereby fulfilling one of the most critical assumptions of weighted‐averaging regression and calibration and its relative, weighted‐averaging partial least‐squares regression. A further 130 surface samples of comparable taphonomy, taxonomic detail and analyst became available as a result of other projects. These 130 samples, all from new lakes, were added to the 191‐lake data set to create the 321‐lake data set. The collection and construction of these data sets are outlined. Numerical analyses involving generalized linear modelling, constrained ordination techniques, weighted‐averaging partial least‐squares regression, and two different cross‐validation procedures are used to asses the effects of increasing the size of the calibration data set from 191 to 321 lakes. The two data sets are used to reconstruct mean July temperature and mean annual precipitation for a Holocene site in northwest Norway and a Lateglacial site in west‐central Norway. Overall, little is to be gained by increasing the modern data set beyond about 200 lakes in terms of modern model performance statistics, but the down‐core reconstructions show less between‐sample variability and are thus potentially more plausible and realistic when based on the 321‐lake data set.     

X-ray transient sources

The galactic distribution and physical nature of X-ray transient sources is investigated. Two types of transients are considered. The observational data on 41 X-ray transient sources are given, and the average parameters of hard and soft X-ray transients are estimated.     

Evidence for focused hot fluid flow within the Britannia Field, offshore Scotland, UK

Fluid inclusion and scanning electron microscope‐cathodoluminescence evidence indicates focused hot, saline, diagenetic fluid flow within the Eastern Flank of the Britannia Field, offshore Scotland, UK. The fluid was sourced from the Andrew Salt Dome, 10 km to the east. The fluids, which promoted quartz cementation of the upper zones within the field, were up to ～30°C hotter and had salinities up to ～10 wt% NaCl equivalent higher than fluids from lower in the reservoir section. During diagenesis hot saline fluids migrated westwards as part of a radiating ‘diagenetic front’ from the Andrew Salt Dome. Structural dip associated with the Eastern Flank of the Fladen Ground Spur impeded the westward movement of the diagenetic fluid. The quartz cements from the upper and lower reservoir zones can be distinguished by morphology. In the upper zones the quartz cements have well‐developed macro‐crystalline zoning and heterogeneous luminescence across the grain. In the lower zones, the cements are much less developed, unzoned and very weakly luminescent. The diagenetic fluids were primarily focused into Zone 45 within the upper reservoir. Furthermore, within the Main Platform Area the most prolific producing zone is Zone 45, indicating the importance of this interval as a permeable flow unit during both diagenetic and production timescales. Within the Eastern Flank, the quartz overgrowths have a major impact on reservoir permeability and thus well productivity. The overgrowths are most extensive in the originally clean sandstones with low clay content. Clay in optimum volumes (5–10%) can inhibit nucleation of the damaging quartz overgrowths without having a detrimental effect on pore connectivity. These observations provide a predictive concept for use in the search for relative reservoir sweetspots within the degraded Eastern Flank.     

Observation of Precipitating Systems over Complex Orography with Meteorological Doppler Radars: A Feasibility Study

Summary  This paper concerns the use of airborne or ground-based Doppler radars to observe precipitating systems over complex orography. As nearly all of the previous experiments involving Doppler radars were conducted over flat surfaces over the continents or the oceans, new techniques are needed firstly to separate ground clutter from meteorological signal and, in the case of airborne Doppler observations, to deduce navigational errors. Secondly, it is necessary to take the atmospheric circulation induced by orography into account in the three-dimensional wind field analysis. Variational techniques are presented to solve these problems. The proposed methods are tested with simulated ground-based and airborne Doppler radar observations for analytic flows over analytic terrains and for numerically simulated wind and reflectivity fields for the Brig event (22 September 1993) of heavy precipitation over the southern flank of the Alps (Cosma and Richard, 1998), and with actual airborne Doppler data relative to weak snow showers over the Rocky Mountains on 12 March 1995. Received March 22, 1999/Revised June 1, 1999