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.     

The Upper Middle Rhine Valley as a risk area

The Upper Middle Rhine Valley, granted the status of a World Heritage site, is well known for its unique inner narrow valley of Quaternary age with its historical legacy of numerous medieval castles and old towns. Less known is that this has always been a risk area of floods and gravitative mass movements. Up to the recent past, mainly ice floods caused enormous damage. The inhabitants of the valley were well aware that they lived in a risk area, but they had learned to handle the flood hazard. With the demise of ice floods over the last 40 years, due to climate change and because of the additional heating of the river water by power plants, the awareness of flood hazards has been much diminished, in contrast to that of potential damage by rockfalls and landslides which were also much feared in the past, though at the local level only. Still in the people’s memory is the Kaub catastrophe of March 10, 1876, when 28 persons were killed by a landslide. Nowadays, even minor rockfalls are a major threat, as they will affect the much-used traffic lines on both banks of the river, in particular the railroads. Therefore, since 2002, on behalf of German Rail (Deutsche Bahn, DB), all problematic slopes have been protected by costly steel-ring nets, although they are an aesthetic problem by UNESCO standards. The feeling of absolute safety created among the public is only subjective, though, as planners are well aware of. Moreover, the impact of modern climate change on slope stability is nearly unknown. Therefore, it is still necessary to develop a risk map for the narrow valley, with emphasis on gravitational hazards.     

Temporal and spatial dynamical simulation of groundwater characteristics in Minqin Oasis

Application scope of geostatistics has been gradually extended from original geologic field to soil science and ecological field, etc. and its successful application results have been widely demonstrated. But little information is reported as to the direct use of geostatistical method to work out the distribu- tion map of groundwater characteristics. In this paper the semivariogram of geostatistics, in combina- tion with GIS, was used to quantitatively study the spatial variation characteristics of groundwater table depth and mineralization degree and their relation to the landuse changes. F test of the used spherical model reached a very significant level, and the theoretical model can well reflect the spatial structural characteristics of groundwater table depth and mineralization degree and achieve an ideal result. This shows that the application of the method in the dynamical simulation of groundwater is feasible. And this paper also provides useful reference for the application of geostatistics in the study of the dy- namical variations of groundwater resources in the oasis.     

A Long-Term Decrease of the Mid-Size Segmentation Lengths Observed in the He <Emphasis Type="SmallCaps">ii</Emphasis> (30.4 nm) Solar EUV Emission

Power spectra of segmentation-cell length (a dominant length scale of EUV emission in the transition region) from full-disk He?ii extreme ultraviolet (EUV) images observed by the Extreme ultraviolet Imaging Telescope (EIT) onboard the Solar and Heliospheric Observatory (SOHO) and the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) during periods of quiet-Sun conditions for a time interval from 1996 to 2015 were analyzed. The spatial power as a function of the spatial frequency from about 0.04 to 0.27 (EIT) or up to 0.48 (AIA) Mm^?1 depends on the distribution of the observed segmentation-cell dimensions – a structure of the solar EUV network. The temporal variations of the spatial power reported by Didkovsky and Gurman (Solar Phys. 289, 153, 2014) were suggested as decreases at the mid-spatial frequencies for the compared spectra when the power curves at the highest spatial frequencies of 0.5 pix^?1 were adjusted to match each other. This approach has been extended in this work to compare spectral ratios at high spatial frequencies expressed in the solar spatial frequency units of Mm^?1. A model of EIT and AIA spatial responses allowed us to directly compare spatial spectral ratios at high spatial frequencies for five years of joint operation of EIT and AIA, from 2010 to 2015. Based on this approach, we represent these ratio changes as a long-term network transformation that may be interpreted as a continuous dissipation of mid-size network structures to the smaller-size structures in the transition region. In contrast to expected cycling of the segmentation-cell dimension structures and associated spatial power in the spectra with the solar cycle, the spectra demonstrate a significant and steady change of the EUV network. The temporal trend across these structural spectra is not critically sensitive to any long-term instrumental changes, e.g. degradation of sensitivity, but to the change of the segmentation-cell dimensions of the EUV network structure.     

Climatic and geographic factors affect ecosystem multifunctionality through biodiversity in the Tibetan alpine grasslands

Ecosystem multifunctionality(EMF), the simultaneous provision of multiple ecosystem functions, is often affected by biodiversity and environmental factors. We know little about how the interactions between biodiversity and environmental factors affect EMF. In this case study, a structural equation model was used to clarify climatic and geographic pathways that affect EMF by varying biodiversity in the Tibetan alpine grasslands. In addition to services related to carbon, nitrogen, and water cycling, forage supply, which is related to plantproductivity and palatability, was included in the EMF index. The results showed that 72% of the variation in EMF could be explained by biodiversity and other environmental factors. The ratio of palatable richness to all species richness explained 8.3% of the EMF variation. We found that air temperature, elevation, and latitude all affected EMF, but in different ways. Air temperature and elevation impacted the aboveground parts of the ecosystem, which included plant height, aboveground biomass, richness of palatable species, and ratio of palatable richness to all species richness. Latitude affected EMF by varying both aboveground and belowground parts of the ecosystem, which included palatable speciesrichness and belowground biomass. Our results indicated that there are still uncertainties in the biodiversity–EMF relationships related to the variable components of EMF, and climatic and geographic factors. Clarification of pathways that affect EMF using structural equation modeling techniques could elucidate the mechanisms by which environmental changes affect EMF.     

Resolving the landfill siting impasse: modelling technocratic and indigenous perspectives using GIS multicriteria approach

Increase in waste generation calls for an effective waste management as this has become a necessity for environmental sustainability. Several methods are adopted in managing waste, which include waste reduction, reuse, thermal treatment, recycling and landfilling. The landfill method is recognised as the most used of all the waste management methods in developing countries such as Ghana. However, the selection of a suitable landfill site is very difficult and tedious. This is because it involves a consideration of many factors such as environmental, topographic, economic, socio-cultural and civil engineering. This research sought to identify a suitable landfill site by applying GIS multicriteria and weighted overlay approach in the Bongo District of Northern Ghana. The analysis relied on criteria and weights provided by the technocrats and the indigenes in the district as a way of demonstrating how landfill siting impasse can be resolved by incorporating the various stakeholders. The results obtained provided clear areas for landfill sites in the study area from the technocratic and the indigenous perspectives. However, the technocratic perspective failed to include an important cultural criterion, sacred groves, as a factor. The indigenous perspective also compromised on the factor related to nearness to residential areas, and is equally not sufficient on its own. The optimal landfill sites, which meets the expectations of both the technocrats and indigenes, was identified. This perspective has produced technically favourable and socio-culturally acceptable landfill site. However, it is recommended an environmental impact assessment (EIA) be conducted to identify the full environmental and social cost of the site. It is concluded that in landfill site selection much attention be given to cultural factors in the same way as the technical factors.     

Understanding the implications of the EU-LULUCF regulation for the wood supply from EU forests to the EU

Background

In June 2018, the European Parliament and Council of the European Union adopted a legislative regulation for incorporating greenhouse gas emissions and removals from Land Use, Land Use Change and Forestry (EU-LULUCF) under its 2030 Climate and Energy Framework. The LULUCF regulation aim to incentivise EU Member States to decrease greenhouse gas emissions and increase removals in the LULUCF sector. The regulation, however, does not set a target for increasing the LULUCF carbon sink, but rather includes a ‘no net debit’ target for LULUCF (Forests and Agricultural soils). For Managed Forest Land (MFL) an accounting framework with capped credits for additional mitigation against a set forest reference level (FRL) was agreed for 2021–2030. The FRL gives the projected future carbon sink in the two compliance periods 2021–2025 and 2026–2030 under “continuation of forest management practices as they were in the reference period 2000–2009”. This FRL was disputed by some Member States as it was perceived to put a limit on their future wood harvesting from MFL. Here we simulated with the EFISCEN European forest model the “continuation of forest management practices” and determined the corresponding wood harvest for 26 EU countries under progressing age classes.

Results

The simulations showed that under “continuation of forest management practices” the harvest (wood removals) in the 26 EU countries as a whole can increase from 420 million m³/year in 2000–2009 to 560 million m³/year in 2050 due to progressing age classes. This implies there is a possibility to increase absolute wood harvests without creating debits compared to the forest reference level. However, the manner in which ‘continuation of forest management’ developed with a progressing age class development over time, meant that in some countries the future harvesting exceeded 90% of the increment. Since this generally is considered to be unsustainable we additionally set a harvesting cut-off as max 90% of increment to be harvested for each individual country as a possible interpretation of sustainability criteria that are included in the regulation. Using this additional limit the projected harvest will only increase to 493 million m³/year.

Conclusions

The worry from Member States (MS) that the FRL will prevent any additional harvesting seems unwarranted. Due to differences between Member States concerning the state of their forest resources, the FRL as a baseline for harvesting works out very differently for the different Member States. The FRL may have other unforeseen consequences which we discuss. Under all scenarios the living forest biomass sink shows a decline. This can be counteracted through incentivising measures under Climate Smart Forestry.

     

On the Principle of Least Interaction Action and the Laplacean satellites of Jupiter and Uranus

The Principle of Least Interaction Action, which explains the observed preference in the Solar System for two-satellite resonant configurations, is shown to apply also to the Laplacean satellites of Jupiter and Uranus, in the sense that these triplet resonant structures lie close to configurations for which the time-mean of the action associated with the mutual interaction of the satellites is an overall minimum. Far from the minimum configuration, significant changes take place in the major semi-axes on time-scales ～10⁶-10⁷y. Both systems require times ～10⁸ y to come close to the minimum configuration; to approach resonance to the observed precision of the Laplace relationship (3×10^?4 for the Uranian case, 2×10^?7 for the Jovian case) requires, for both systems, a time closely comparable with the age of the solar system.     

Picophytoplankton and bacterioplankton in the Mississippi River plume and its adjacent waters

Picoplankton abundance and distribution in the Mississippi River plume and its adjacent waters were studied during two cruises in April (high discharge) and October (low discharge) 2000 using flow cytometry. Concentrations of photosynthetic picoplankton,Synechococcus and picoeukaryotes were low in the turbid plume water but high in the coastal waters—i.e., the green waters resulting from mixing of river and oceanic waters. In this region, three types ofSynechococcus, characterized by their phycoerythrin chromophore composition, were found:Synechococcus cells with a low phycourobilin to phycoerythrobilin ratio (PUB:PEB) occurred throughout the region and dominated the totalSymechococcus abundance during both seasons; high PUB:PEB cells, which are the dominant strains in the open or blue ocean, occurred only at the outer shelf stations; and PEB-onlySynechococcus were abundant in most of the surveyed area during april, but were not observed during October.Prochlorococcus cyanobacteria only occurred at the oceanic stations, but extended farther inshore in October compared to April. This was a consequence of the reduced discharge and plume size during October. Picophytoplankton were a less important component of total phytoplankton biomass in the turbid river water and more important in the oligotrophic Gulf water. Seasonally, the contribution of picophytoplankton to total phytoplankton biomass in the surveyed area was higher during low discharge in October than during high discharge in April, even though the spring 2000 river discharge was unusually low and might not present a typical high discharge scenario. The abundance of heterotrophic bacteria was weakly correlated to chlorophylla (chla) concentration, but better correlated to picophytoplankton biomass. A higher proportion of High DNA bacteria occurred in the river-impacted regions during both seasons, with the ratio of High DNA bacteria to Low DNA bacteria significantly higher in April.     

Non-Linear Gravitational Clustering Using the Zel'dovich Approximation

As an alternative to computationally expensive N-body simulations for gravitional clustering, the Zel'dovich approximation (ZA) was studied in 3D, 2D and 1D. Plots of the density contrast were compared against linear theory and the exact solution. The ZA was found to perform very well in the linear regime, better than linear theory, and to give a good approximation well into the non-linear regime. This revised version was published online in July 2006 with corrections to the Cover Date.