Quantifying rock fabrics: a test of autocorrelation of the spatial distribution of cristals

A novel test of spatial independence of the distribution of crystals or phases in rocks based on compositional statistics is introduced. It improves and generalizes the common joins-count statistics known from map analysis in geographic information systems. Assigning phases independently to objects in RD is modelled by a single-trial multinomial random function Z(x), where the probabilities of phases add to one and are explicitly modelled as compositions in the K-part simplex SK. Thus, apparent inconsistencies of the tests based on the conventional joins{count statistics and their possibly contradictory interpretations are avoided. In practical applications we assume that the probabilities of phases do not depend on the location but are identical everywhere in the domain of de nition. Thus, the model involves the sum of r independent identical multinomial distributed 1-trial random variables which is an r-trial multinomial distributed random variable. The probabilities of the distribution of the r counts can be considered as a composition in the Q-part simplex SQ. They span the so called Hardy-Weinberg manifold H that is proved to be a K-1-affine subspace of SQ. This is a generalisation of the well-known Hardy-Weinberg law of genetics. If the assignment of phases accounts for some kind of spatial dependence, then the r-trial probabilities do not remain on H. This suggests the use of the Aitchison distance between observed probabilities to H to test dependence. Moreover, when there is a spatial uctuation of the multinomial probabilities, the observed r-trial probabilities move on H. This shift can be used as to check for these uctuations. A practical procedure and an algorithm to perform the test have been developed. Some cases applied to simulated and real data are presented. Key words: Spatial distribution of crystals in rocks, spatial distribution of phases, joins-count statistics, multinomial distribution, Hardy-Weinberg law, Hardy-Weinberg manifold, Aitchison geometry

Spatial Inequalities and Social Utility: Mobility Efforts and Accessibility in Greater Santiago

Emergent phenomena such as urban sprawl, travel intensification and loss of cohesion in contemporary metropolises, impose stronger constraints on its inhabitants. Among them, travel and location capabilities become a fundamental factor of social integration and a multiplier of income inequalities. The simultaneous analysis of housing-travel efforts and accessibility to urban opportunities in Greater Santiago shows that these dimensions are closely related and exert an important influence on spatial mobility and inequalities among its inhabitants. Furthermore, a theoretical model of displacements, considering income and location, confirms the importance of proximity and non-motorized transport in order to optimize daily mobility strategies of households. Overall, the empirical and theoretical results presented show the need to implement coordinated planning strategies between the housing and transport sectors, addressing not only travel acceleration, but mainly the consistency between accommodation and opportu  ties location. The creation of such planning tools could be a more sustainable alternative than current growth trends in Greater Santiago.

Biased representation of disturbance rates in the roadside sampling frame in boreal forests: implications for monitoring design

The North American Breeding Bird Survey (BBS) is the principal source of data to inform researchers about the status of and trend for boreal forest birds. Unfortunately, little BBS coverage is available in the boreal forest, where increasing concern over the status of species breeding there has increased interest in northward expansion of the BBS. However, high disturbance rates in the boreal forest may complicate roadside monitoring. If the roadside sampling frame does not capture variation in disturbance rates because of either road placement or the use of roads for resource extraction, biased trend estimates might result. In this study, we examined roadside bias in the proportional representation of habitat disturbance via spatial data on forest “loss,” forest fires, and anthropogenic disturbance. In each of 455 BBS routes, the area disturbed within multiple buffers away from the road was calculated and compared against the area disturbed in degree blocks and BBS strata. We found a nonlinear relationship between bias and distance from the road, suggesting forest loss and forest fires were underrepresented below 75 and 100 m, respectively. In contrast, anthropogenic disturbance was overrepresented at distances below 500 m and underrepresented thereafter. After accounting for distance from road, BBS routes were reasonably representative of the degree blocks they were within, with only a few strata showing biased representation. In general, anthropogenic disturbance is overrepresented in southern strata, and forest fires are underrepresented in almost all strata. Similar biases exist when comparing the entire road network and the subset sampled by BBS routes against the amount of disturbance within BBS strata; however, the magnitude of biases differed. Based on our results, we recommend that spatial stratification and rotating panel designs be used to spread limited BBS and off-road sampling effort in an unbiased fashion and that new BBS routes be established where sufficient road coverage exists.

Spatial variability of flow statistics within regular building arrays

Turbulence statistics obtained by direct numerical simulations are analysed to investigate spatial heterogeneity within regular arrays of building-like cubical obstacles. Two different array layouts are studied, staggered and square, both at a packing density of λp=0.25 . The flow statistics analysed are mean streamwise velocity ( u− ), shear stress ( u′w′−−−− ), turbulent kinetic energy (k) and dispersive stress fraction ( u˜w˜ ). The spatial flow patterns and spatial distribution of these statistics in the two arrays are found to be very different. Local regions of high spatial variability are identified. The overall spatial variances of the statistics are shown to be generally very significant in comparison with their spatial averages within the arrays. Above the arrays the spatial variances as well as dispersive stresses decay rapidly to zero. The heterogeneity is explored further by separately considering six different flow regimes identified within the arrays, described here as: channelling region, constricted region, intersection region, building wake region, canyon region and front-recirculation region. It is found that the flow in the first three regions is relatively homogeneous, but that spatial variances in the latter three regions are large, especially in the building wake and canyon regions. The implication is that, in general, the flow immediately behind (and, to a lesser extent, in front of) a building is much more heterogeneous than elsewhere, even in the relatively dense arrays considered here. Most of the dispersive stress is concentrated in these regions. Considering the experimental difficulties of obtaining enough point measurements to form a representative spatial average, the error incurred by degrading the sampling resolution is investigated. It is found that a good estimate for both area and line averages can be obtained using a relatively small number of strategically located sampling points.

Sampling uncertainties in surface radiation budget calculations in RADAGAST

In the Radiative Atmospheric Divergence Using ARM Mobile Facility GERB and AMMA Stations (RADAGAST) project we calculate the divergence of radiative flux across the atmosphere by comparing fluxes measured at each end of an atmospheric column above Niamey, in the African Sahel region. The combination of broadband flux measurements from geostationary orbit and the deployment for over 12 months of a comprehensive suite of active and passive instrumentation at the surface eliminates a number of sampling issues that could otherwise affect divergence calculations of this sort. However, one sampling issue that challenges the project is the fact that the surface flux data are essentially measurements made at a point, while the top-of-atmosphere values are taken over a solid angle that corresponds to an area at the surface of some 2500 km2. Variability of cloud cover and aerosol loading in the atmosphere mean that the downwelling fluxes, even when averaged over a day, will not be an exact match to the area-averaged value over that larger area, although we might expect that it is an unbiased estimate thereof. The heterogeneity of the surface, for example, fixed variations in albedo, further means that there is a likely systematic difference in the corresponding upwelling fluxes. In this paper we characterize and quantify this spatial sampling problem. We bound the root-mean-square error in the downwelling fluxes by exploiting a second set of surface flux measurements from a site that was run in parallel with the main deployment. The differences in the two sets of fluxes lead us to an upper bound to the sampling uncertainty, and their correlation leads to another which is probably optimistic as it requires certain other conditions to be met. For the upwelling fluxes we use data products from a number of satellite instruments to characterize the relevant heterogeneities and so estimate the systematic effects that arise from the flux measurements having to be taken at a single point. The sampling uncertainties vary with the season, being higher during the monsoon period. We find that the sampling errors for the daily average flux are small for the shortwave irradiance, generally less than 5 W m−2, under relatively clear skies, but these increase to about 10 W m−2 during the monsoon. For the upwelling fluxes, again taking daily averages, systematic errors are of order 10 W m−2 as a result of albedo variability. The uncertainty on the longwave component of the surface radiation budget is smaller than that on the shortwave component, in all conditions, but a bias of 4 W m−2 is calculated to exist in the surface leaving longwave flux.

The spatial distribution and evolution characteristics of North Atlantic cyclones

A climatology of extratropical cyclones is produced using an objective method of identifying cyclones based on gradients of 1-km height wet-bulb potential temperature. Cyclone track and genesis density statistics are analyzed and this method is found to compare well with other cyclone identification methods. The North Atlantic storm track is reproduced along with the major regions of genesis. Cyclones are grouped according to their genesis location and the corresponding lysis regions are identified. Most of the cyclones that cross western Europe originate in the east Atlantic where the baroclinicity and the sea surface temperature gradients are weak compared to the west Atlantic. East Atlantic cyclones also have higher 1-km height relative vorticity and lower mean sea level pressure at their genesis point than west Atlantic cyclones. This is consistent with the hypothesis that they are secondary cyclones developing on the trailing fronts of preexisting “parent” cyclones. The evolution characteristics of composite west and east Atlantic cyclones have been compared. The ratio of their upper- to lower-level forcing indicates that type B cyclones are predominant in both the west and east Atlantic, with strong upper- and lower-level features. Among the remaining cyclones, there is a higher proportion of type C cyclones in the east Atlantic, whereas types A and C are equally frequent in the west Atlantic.

Estimating surface CO2 fluxes from space-borne dry air mole fraction observations using an Ensemble Kalman filter

We have developed an ensemble Kalman Filter (EnKF) to estimate 8-day regional surface fluxes of CO2 from space-borne CO2 dry-air mole fraction observations (XCO2) and evaluate the approach using a series of synthetic experiments, in preparation for data from the NASA Orbiting Carbon Observatory (OCO). The 32-day duty cycle of OCO alternates every 16 days between nadir and glint measurements of backscattered solar radiation at short-wave infrared wavelengths. The EnKF uses an ensemble of states to represent the error covariances to estimate 8-day CO2 surface fluxes over 144 geographical regions. We use a 12×8-day lag window, recognising that XCO2 measurements include surface flux information from prior time windows. The observation operator that relates surface CO2 fluxes to atmospheric distributions of XCO2 includes: a) the GEOS-Chem transport model that relates surface fluxes to global 3-D distributions of CO2 concentrations, which are sampled at the time and location of OCO measurements that are cloud-free and have aerosol optical depths <0.3; and b) scene-dependent averaging kernels that relate the CO2 profiles to XCO2, accounting for differences between nadir and glint measurements, and the associated scene-dependent observation errors. We show that OCO XCO2 measurements significantly reduce the uncertainties of surface CO2 flux estimates. Glint measurements are generally better at constraining ocean CO2 flux estimates. Nadir XCO2 measurements over the terrestrial tropics are sparse throughout the year because of either clouds or smoke. Glint measurements provide the most effective constraint for estimating tropical terrestrial CO2 fluxes by accurately sampling fresh continental outflow over neighbouring oceans. We also present results from sensitivity experiments that investigate how flux estimates change with 1) bias and unbiased errors, 2) alternative duty cycles, 3) measurement density and correlations, 4) the spatial resolution of estimated flux estimates, and 5) reducing the length of the lag window and the size of the ensemble. At the revision stage of this manuscript, the OCO instrument failed to reach its orbit after it was launched on 24 February 2009. The EnKF formulation presented here is also applicable to GOSAT measurements of CO2 and CH4.

The spatial prediction of soil mineral N and potentially available N using elevation

The precision farmer wants to manage the variation in soil nutrient status continuously, which requires reliable predictions at places between sampling sites. Ordinary kriging can be used for prediction if the data are spatially dependent and there is a suitable variogram model. However, even if data are spatially correlated, there are often few soil sampling sites in relation to the area to be managed. If intensive ancillary data are available and these are coregionalized with the sparse soil data, they could be used to increase the accuracy of predictions of the soil properties by methods such as cokriging, kriging with external drift and regression kriging. This paper compares the accuracy of predictions of the plant available N properties (mineral N and potentially available N) for two arable fields in Bedfordshire, United Kingdom, from ordinary kriging, cokriging, kriging with external drift and regression kriging. For the last three, intensive elevation data were used with the soil data. The mean squared errors of prediction from these methods of kriging were determined at validation sites where the values were known. Kriging with external drift resulted in the smallest mean squared error for two of the three properties examined, and cokriging for the other. The results suggest that the use of intensive ancillary data can increase the accuracy of predictions of soil properties in arable fields provided that the variables are related spatially. (c) 2005 Elsevier B.V. All rights reserved.

Exploring the spatial relations between soil physical properties and apparent electrical conductivity

Relations between the apparent electrical conductivity of the soil (ECa) and top- and sub-soil physical properties were examined for two arable fields in southern England (Crowmarsh Battle Farms and the Yattendon Estate). The spatial variation of ECa and the soil properties was explored geostatistically. The variogram ranges showed that ECa varied on a similar spatial scale to many of the soil physical properties in both fields. Several features in the map of kriged predictions of ECa were also evident in maps of the soil properties. In addition, the correlation coefficients showed a strong relation between ECa and several soil properties. A moving correlation analysis enabled differences in the relations between ECa and the soil properties to be examined within the fields. The results indicated that relations were inconsistent; they were stronger in some areas than others. A regression of ECa on the principal component scores of the leading components for both fields showed that the first two components accounted for a large proportion of the variance in ECa, whereas the others accounted for little or none. For Crowmarsh topsoil sand and clay, loss on ignition and volumetric water measured in the autumn had large correlations on the first component, and for Yattendon they were large for topsoil sand and clay, and autumn and spring volumetric water. The cross-variograms suggested strong coregionalization between ECa and several soil physical properties; in particular subsoil sand and silt at Crowmarsh, and subsoil sand and clay at Yattendon. The structural correlations from the linear model of coregionalization confirmed the strength of the relations between ECa and the subsoil properties. Nevertheless, no one property was consistently important for both fields. Although a map of ECa can indicate the general patterns of spatial variation in the soil, it is not a substitute for information on soil properties obtained by sampling and analysing the soil. Nevertheless, it could be used to guide further sampling. (c) 2005 Elsevier B.V. All rights reserved.

Exploring the spatial relations between soil properties and electro-magnetic induction (EMI) and the implications for management

The relations between soil electrical conductivity (ECa) and top- and sub-soil physical properties were examined for an arable field in England. The correlation coefficients between ECa and the soil particle size fractions were large and their cross variograms showed that the coregionalization was also strong. The coregionalization was stronger for the subsoil properties than for the topsoil, the reverse to the correlation coefficients. The relations between ECa and some soil properties, such as clay and water content, appear complex and emphasize that a map of ECa cannot substitute for sampling the soil.

Variograms of ancillary data to aid sampling for soil surveys

To provide reliable estimates for mapping soil properties for precision agriculture requires intensive sampling and costly laboratory analyses. If the spatial structure of ancillary data, such as yield, digital information from aerial photographs, and soil electrical conductivity (EC) measurements, relates to that of soil properties they could be used to guide the sampling intensity for soil surveys. Variograins of permanent soil properties at two study sites on different parent materials were compared with each other and with those for ancillary data. The ranges of spatial dependence identified by the variograms of both sets of properties are of similar orders of magnitude for each study site, Maps of the ancillary data appear to show similar patterns of variation and these seem to relate to those of the permanent properties of the soil. Correlation analysis has confirmed these relations. Maps of kriged estimates from sub-sampled data and the original variograrns showed that the main patterns of variation were preserved when a sampling interval of less than half the average variogram range of ancillary data was used. Digital data from aerial photographs for different years and EC appear to show a more consistent relation with the soil properties than does yield. Aerial photographs, in particular those of bare soil, seem to be the most useful ancillary data and they are often cheaper to obtain than yield and EC data.

Comparing sampling needs for variograms of soil properties computed by the method of moments and residual maximum likelihood

It has been generally accepted that the method of moments (MoM) variogram, which has been widely applied in soil science, requires about 100 sites at an appropriate interval apart to describe the variation adequately. This sample size is often larger than can be afforded for soil surveys of agricultural fields or contaminated sites. Furthermore, it might be a much larger sample size than is needed where the scale of variation is large. A possible alternative in such situations is the residual maximum likelihood (REML) variogram because fewer data appear to be required. The REML method is parametric and is considered reliable where there is trend in the data because it is based on generalized increments that filter trend out and only the covariance parameters are estimated. Previous research has suggested that fewer data are needed to compute a reliable variogram using a maximum likelihood approach such as REML, however, the results can vary according to the nature of the spatial variation. There remain issues to examine: how many fewer data can be used, how should the sampling sites be distributed over the site of interest, and how do different degrees of spatial variation affect the data requirements? The soil of four field sites of different size, physiography, parent material and soil type was sampled intensively, and MoM and REML variograms were calculated for clay content. The data were then sub-sampled to give different sample sizes and distributions of sites and the variograms were computed again. The model parameters for the sets of variograms for each site were used for cross-validation. Predictions based on REML variograms were generally more accurate than those from MoM variograms with fewer than 100 sampling sites. A sample size of around 50 sites at an appropriate distance apart, possibly determined from variograms of ancillary data, appears adequate to compute REML variograms for kriging soil properties for precision agriculture and contaminated sites. (C) 2007 Elsevier B.V. All rights reserved.

The importance of precision in sampling sludges, biowastes and treated soils in a regulatory framework

As part of the European Commission (EC)'s revision of the Sewage Sludge Directive and the development of a Biowaste Directive, there was recognition of the difficulty of comparing data from Member States (MSs) because of differences in sampling and analytical procedures. The 'HORIZONTAL' initiative, funded by the EC and MSs, seeks to address these differences in approach and to produce standardised procedures in the form of CEN standards. This article is a preliminary investigation into aspects of the sampling of biosolids, composts and soils to which there is a history of biosolid application. The article provides information on the measurement uncertainty associated with sampling from heaps, large bags and pipes and soils in the landscape under a limited set of conditions, using sampling approaches in space and time and sample numbers based on procedures widely used in the relevant industries and when sampling similar materials. These preliminary results suggest that considerably more information is required before the appropriate sample design, optimum number of samples, number of samples comprising a composite, and temporal and spatial frequency of sampling might be recommended to achieve consistent results of a high level of precision and confidence. (C) 2004 Elsevier Ltd. All rights reserved.

The Dubawnt Lake palaeo-ice stream: evidence for dynamic ics sheet behaviour on the Canadian Shield and insights regarding the controls on ice-stream location and vigour

We report evidence for a major ice stream that operated over the northwestern Canadian Shield in the Keewatin Sector of the Laurentide Ice Sheet during the last deglaciation 9000-8200 (uncalibrated) yr BP. It is reconstructed at 450 km in length, 140 km in width, and had an estimated catchment area of 190000 km. Mapping from satellite imagery reveals a suite of bedforms ('flow-set') characterized by a highly convergent onset zone, abrupt lateral margins, and where flow was presumed to have been fastest, a remarkably coherent pattern of mega-scale glacial lineations with lengths approaching 13 km and elongation ratios in excess of 40:1. Spatial variations in bedform elongation within the flow-set match the expected velocity field of a terrestrial ice stream. The flow pattern does not appear to be steered by topography and its location on the hard bedrock of the Canadian Shield is surprising. A soft sedimentary basin may have influenced ice-stream activity by lubricating the bed over the downstream crystalline bedrock, but it is unlikely that it operated over a pervasively deforming till layer. The location of the ice stream challenges the view that they only arise in deep bedrock troughs or over thick deposits of 'soft' fine-grained sediments. We speculate that fast ice flow may have been triggered when a steep ice sheet surface gradient with high driving stresses contacted a proglacial lake. An increase in velocity through calving could have propagated fast ice flow upstream (in the vicinity of the Keewatin Ice Divide) through a series of thermomechanical feedback mechanisms. It exerted a considerable impact on the Laurentide Ice Sheet, forcing the demise of one of the last major ice centres.

Airborne measurements of the spatial distribution of aerosol chemical composition across Europe and evolution of the organic fraction

The spatial distribution of aerosol chemical composition and the evolution of the Organic Aerosol (OA) fraction is investigated based upon airborne measurements of aerosol chemical composition in the planetary boundary layer across Europe. Sub-micron aerosol chemical composition was measured using a compact Time-of-Flight Aerosol Mass Spectrometer (cToF-AMS). A range of sampling conditions were evaluated, including relatively clean background conditions, polluted conditions in North-Western Europe and the near-field to far-field outflow from such conditions. Ammonium nitrate and OA were found to be the dominant chemical components of the sub-micron aerosol burden, with mass fractions ranging from 20--50% each. Ammonium nitrate was found to dominate in North-Western Europe during episodes of high pollution, reflecting the enhanced NO_x and ammonia sources in this region. OA was ubiquitous across Europe and concentrations generally exceeded sulphate by 30--160%. A factor analysis of the OA burden was performed in order to probe the evolution across this large range of spatial and temporal scales. Two separate Oxygenated Organic Aerosol (OOA) components were identified; one representing an aged-OOA, termed Low Volatility-OOA and another representing fresher-OOA, termed Semi Volatile-OOA on the basis of their mass spectral similarity to previous studies. The factors derived from different flights were not chemically the same but rather reflect the range of OA composition sampled during a particular flight. Significant chemical processing of the OA was observed downwind of major sources in North-Western Europe, with the LV-OOA component becoming increasingly dominant as the distance from source and photochemical processing increased. The measurements suggest that the aging of OA can be viewed as a continuum, with a progression from a less oxidised, semi-volatile component to a highly oxidised, less-volatile component. Substantial amounts of pollution were observed far downwind of continental Europe, with OA and ammonium nitrate being the major constituents of the sub-micron aerosol burden. Such anthropogenically perturbed air masses can significantly perturb regional climate far downwind of major source regions.