Additive Log-ratio Transformation Research Articles

Robust score matching for compositional data

The restricted polynomially-tilted pairwise interaction (RPPI) distribution gives a flexible model for compositional data. It is particularly well-suited to situations where some of the marginal distributions of the components of a composition are concentrated near zero, possibly with right skewness. This article develops a method of tractable robust estimation for the model by combining two ideas. The first idea is to use score matching estimation after an additive log-ratio transformation. The resulting estimator is automatically insensitive to zeros in the data compositions. The second idea is to incorporate suitable weights in the estimating equations. The resulting estimator is additionally resistant to outliers. These properties are confirmed in simulation studies where we further also demonstrate that our new outlier-robust estimator is efficient in high concentration settings, even in the case when there is no model contamination. An example is given using microbiome data. A user-friendly R package accompanies the article.

A compositional data model to predict the isotope distribution for average peptides using a compositional spline model.

We propose an updated approach for approximating the isotope distribution of average peptides given their monoisotopic mass. Our methodology involves in-silico cleavage of the entire UNIPROT database of human-reviewed proteins using Trypsin, generating a theoretical peptide dataset. The isotope distribution is computed using BRAIN. We apply a compositional data modelling strategy that utilizes an additive log-ratio transformation for the isotope probabilities followed by a penalized spline regression. Furthermore, due to the impact of the number of sulphur atoms on the course of the isotope distribution, we develop separate models for peptides containing zero up to five sulphur atoms. Additionally, we propose three methods to estimate the number of sulphur atoms based on an observed isotope distribution. The performance of the spline models and the sulphur prediction approaches is evaluated using a mean squared error and a modified Pearson's χ2 goodness-of-fit measure on an experimental UPS2 data set. Our analysis reveals that the variability in spectral accuracy, that is, the variability between MS1 scans, contributes more to the errors than the approximation of the theoretical isotope distribution by our proposed average peptide model. Moreover, we find that the accuracy of predicting the number of sulphur atoms based on the observed isotope distribution is limited by measurement accuracy.

Clustering microbiome data using mixtures of logistic normal multinomial models

Discrete data such as counts of microbiome taxa resulting from next-generation sequencing are routinely encountered in bioinformatics. Taxa count data in microbiome studies are typically high-dimensional, over-dispersed, and can only reveal relative abundance therefore being treated as compositional. Analyzing compositional data presents many challenges because they are restricted to a simplex. In a logistic normal multinomial model, the relative abundance is mapped from a simplex to a latent variable that exists on the real Euclidean space using the additive log-ratio transformation. While a logistic normal multinomial approach brings flexibility for modeling the data, it comes with a heavy computational cost as the parameter estimation typically relies on Bayesian techniques. In this paper, we develop a novel mixture of logistic normal multinomial models for clustering microbiome data. Additionally, we utilize an efficient framework for parameter estimation using variational Gaussian approximations (VGA). Adopting a variational Gaussian approximation for the posterior of the latent variable reduces the computational overhead substantially. The proposed method is illustrated on simulated and real datasets.

Elemental Abundances of Moon Samples Based on Statistical Distributions of Analytical Data

The successful return of Chang’E-5 (CE5) samples urges the hot topic of the study of the Moon in geochemistry. The elemental data of the analyzed moon samples reported in the literature were collected to determine the elemental abundances in moon samples. Based on 2365 analytical records of moon samples from ten missions of Apollo, Luna, and CE5, elemental abundances of 11 major oxides including Cr2O3, 50 trace elements including Ti, P, Mn, Cr, and 15 rare earth elements (REEs) including Y are derived based on statistical distributions of normal, log-normal, and additive log-ratio transformation, respectively. According to the value of 13.5% CaO content, moon samples are classified into two types, as low-Ca and high-Ca samples, whose elemental abundances are also calculated respectively based on the methods used in the total moon samples. With respect to the mid-ocean ridge basalt (MORB) of the Earth, moon samples (including the Moon, low-Ca, and high-Ca samples) are rich in Cr, REEs, Th, U, Pb, Zr, Hf, Cs, Ba, W, and Be and poor in Na, V, Cu, and Zn in terms of their concentrations, and are enriched in Cr and depleted in Na, K, Rb, P, V, Cu, Zn in spider diagrams. The CE5 sample is a low-Ca type of moon sample and is clearly rich in Ti, Fe, Mn, P, Sc, REEs, Th, U, Nb, Ta, Zr, Hf, Sr, Ba, W, and Be and poor in Mg, Al, Cr, and Ni in terms of their concentrations relative to the moon or the low-Ca samples. If compared with the moon sample, the CE5 sample is also clearly rich in K, REE, and P.

Iron Supplementation May Selectively Reprofile the Gut Microbiome in Iron-Deficient Bangladeshi Infants

Children in low- and middle-income countries (LMICs) have a high burden of anemia, much of which is attributable to iron deficiency. The World Health Organization (WHO) recommends universal iron interventions in preschool-aged children in countries where there is a high anemia prevalence. However, oral iron supplementation is associated with increased risks of infection, including diarrhea. In small studies in Africa, iron has been shown to reprofile the intestinal microbiota leading to a reduction in commensal bacteria and an increase in pathogenic taxa. Gut dysbiosis has been implicated in the pathogenesis of gastrointestinal, autoimmune and inflammatory disease. The BRISC (Benefits and Risks of Iron Interventions in Children) trial was a double-blind, placebo-controlled randomized controlled trial of oral iron supplementation in 3,300 infants in Bangladesh. Children were randomized to receive one of iron syrup, iron-containing multiple micronutrient powder (MNP) or placebo daily for three months. The primary outcome of the trial was child cognitive development. Key findings from the trial were an improvement in hematological indices with iron but no effect on the functional outcomes assessed (Pasricha et al New Engl J Med 2021). We aimed to study the effect of iron on microbiome composition, diversity and function in the BRISC participants. To achieve this aim we undertook a substudy in which we collected stool samples from 925 children at the three time points of the main BRISC trial: at recruitment, end of intervention and at nine-month follow up. DNA was extracted and analyzed by 16S ribosomal RNA gene (rRNA) amplicon sequencing (2,339 samples across three timepoints) and shotgun metagenomics (965 samples across three timepoints). Episodes of infection were documented as per the main BRISC trial and included diarrhea, respiratory symptoms, antibiotic use, and clinic/hospital visits. The V4 hypervariable region of the 16S rRNA gene was amplified and sequenced on the Illumina MiSeq instrument together with negative and positive controls. Demultiplexed forward and reverse FASTQ files for each sample were trimmed and processed using the DADA2 package in RStudio, and taxonomy was assigned using the SILVA 138 SSU Ref NR 99 reference database. Control samples and samples with fewer than 500 reads were removed (2,284 samples met this minimum read threshold). Taxonomic, alpha diversity and beta diversity measures were conducted using phyloseq and microbiomeSeq packages in RStudio. Differential abundance was calculated by two separate methods: i. limma voom (using trimmed mean of M values [TMM] normalization and log transformation) and ii. ANCOM-BC (using additive log-ratio transformation). Prior to implementing differential abundance methods a filter was applied such that operational taxonomic units (OTUs) found in under 10% of samples were pruned from the samples. As previously reported, there was no overall significant increase in diarrhea incidence among participants receiving iron compared to those given placebo among BRISC trial participants. Baseline iron deficiency, anemia and iron deficiency anemia prevalence among substudy participants was 33%, 42% and 26% respectively. 16S rRNA analysis demonstrated that recent antibiotic (12% of children at end of intervention) was associated with a significant reduction in alpha diversity. Accordingly, analysis was conducted to exclude recent antibiotic use from analysis by intervention arm. Using this analysis, there were no significant differences in alpha or beta diversity between trial intervention groups at the end of intervention (alpha diversity by Shannon index shown in Figure 1). Members of Ruminococcus torques group (limma voom and ANCOM-BC) and Leuconostoc (limma voom only) were more abundant in the intestinal microbiota of children randomized to iron, but no genus was found to be differentially abundant when controlling for multiple comparisons. However, several bacterial genera were differentially abundant in children who were iron deficient at baseline who received iron. Two forms of analyses (Limma voom and ANCOM-BC) showed agreement in finding a reduction in Sutterella and Lactococcus species in iron deficient children receiving iron. These results are shown in Table 1. These data indicate that reprofiling of the intestinal microbiota in response to iron supplementation is dependent on baseline host iron status. Figure 1View largeDownload PPTFigure 1View largeDownload PPT Close modal

Colombian soil texture: building a spatial ensemble model

Abstract. Texture is a fundamental soil property for multiple applications in environmental and earth sciences. Knowing its spatial distribution allows a better understanding of the response of soil conditions to changes in the environment, such as land use. This paper describes the technical development of Colombia's first texture maps, obtained via a spatial ensemble of national and global digital soil mapping products. This work compiles a new database with 4203 soil profiles, which were harmonized at five standard depths (0–5, 5–15, 15–30, 30–60, and 60–100 cm) and standardized with additive log ratio (ALR) transformation. A compilation of 83 covariates was developed and harmonized at 1 km2 of spatial resolution. Ensemble machine learning (EML) algorithms (MACHISPLIN and landmap) were trained to predict the distribution of soil particle size fractions (PSFs) (clay, sand, and silt), and a comparison with SoilGrids (SG) products was performed. Finally, a spatial ensemble function was created to identify the smallest prediction errors between EML and SG. Our results are the first effort to build a national texture map (clay, sand, and silt fractions) based on digital soil mapping in Colombia. The results of EML algorithms showed that their accuracies were very similar at each standard depth, and were more accurate than SG. The largest improvement with the spatial ensemble was found at the first layer (0–5 cm). EML predictions were frequently selected for each PSF and depth in the total area; however, SG predictions were better when increasing soil depth in some specific regions. The final error distribution in the study area showed that sand presented higher absolute error values than clay and silt fractions, specifically in eastern Colombia. The spatial distribution of soil texture in Colombia is a potential tool to provide information for water-related applications, ecosystem services, and agricultural and crop modeling. However, future efforts need to improve aspects such as treating abrupt changes in the texture between depths and unbalanced data. Our results and the compiled database (https://doi.org/10.6073/pasta/3f91778c2f6ad46c3cc70b61f02532db, Varón-Ramírez and Araujo-Carrillo, 2022, https://doi.org/10.6073/pasta/d6c0bf5847aa40836b42dcc3e0ea874e, Varón-Ramírez et al., 2022) provide new insights to solve some of the aforementioned issues.

Compositional Data Analysis of Microbiome and Any-Omics Datasets: A Validation of the Additive Logratio Transformation.

Microbiome and omics datasets are, by their intrinsic biological nature, of high dimensionality, characterized by counts of large numbers of components (microbial genes, operational taxonomic units, RNA transcripts, etc.). These data are generally regarded as compositional since the total number of counts identified within a sample is irrelevant. The central concept in compositional data analysis is the logratio transformation, the simplest being the additive logratios with respect to a fixed reference component. A full set of additive logratios is not isometric, that is they do not reproduce the geometry of all pairwise logratios exactly, but their lack of isometry can be measured by the Procrustes correlation. The reference component can be chosen to maximize the Procrustes correlation between the additive logratio geometry and the exact logratio geometry, and for high-dimensional data there are many potential references. As a secondary criterion, minimizing the variance of the reference component's log-transformed relative abundance values makes the subsequent interpretation of the logratios even easier. On each of three high-dimensional omics datasets the additive logratio transformation was performed, using references that were identified according to the abovementioned criteria. For each dataset the compositional data structure was successfully reproduced, that is the additive logratios were very close to being isometric. The Procrustes correlations achieved for these datasets were 0.9991, 0.9974, and 0.9902, respectively. We thus demonstrate, for high-dimensional compositional data, that additive logratios can provide a valid choice as transformed variables, which (a) are subcompositionally coherent, (b) explain 100% of the total logratio variance and (c) come measurably very close to being isometric. The interpretation of additive logratios is much simpler than the complex isometric alternatives and, when the variance of the log-transformed reference is very low, it is even simpler since each additive logratio can be identified with a corresponding compositional component.

Relative associations of abdominal and thigh compositions with cardiometabolic diseases in African Caribbean men.

BackgroundRegional body compositions are differentially associated with cardiometabolic risk factors. Simultaneous inclusion of both upper and lower body composition predictors in models is not often done, and studies which do include both measures (1) tend to exclude some tissue(s) of potential metabolic relevance, and (2) have used study populations with underrepresentation of individuals with African ancestries. Further, most body composition analyses do not employ compositional data analytic approaches, which may result in spurious associations.ObjectiveThe objective of this analysis was to assess associations of abdominal and thigh adipose (AT) and muscle tissues with hypertension and type 2 diabetes using compositional data analytic methods.Research Design and MethodsThis cross‐sectional analysis included 610 African Caribbean men (median age: 62 years; mean BMI: 27.8 kg/m2). Abdominal (three components: subcutaneous [ASAT] and visceral [VAT] AT, ‘other’ abdominal tissue) and mid‐thigh (four components: subcutaneous and intermuscular AT, muscle, bone) compositions were measured by computed tomography; additive log ratio transformations were applied to each composition. Regression models were used to simultaneously assess associations of abdominal and thigh component ratios with continuous risk factors (blood pressures, fasting glucose and insulin, HOMA‐IR) and disease categories.ResultsA two‐fold increase in ASAT:‘Other’ ratio was associated with higher continuous risk factors and with odds of being in a higher hypertension (OR: 1.77, 95%CI: 1.10–2.84) or diabetes (OR: 1.81, 95%CI: 1.06–3.10) category. A two‐fold increased VAT ratio was only associated with higher log‐insulin and log‐HOMA‐IR (β = 0.10, p < 0.05 for both), while a two‐fold increased thigh muscle:bone ratio was associated with a lower diabetes category (OR: 0.37, 95%CI: 0.14–1.01).ConclusionsThese findings support ASAT as a significant driver of cardiometabolic disease in African Ancestry populations, independent of other abdominal and thigh tissues.

Bioaccessibility and provenance of heavy metals in the park dust in a coastal city of southeast China

Bioaccessibility and provenance of heavy metals (V, Cr, Co, Ni, Cu, Zn, As, Cd, Ba, Pb) in the park dusts were investigated. The enrichment factors (EFs) indicated that Cd, Cu, and Zn were substantially higher enriched than the other heavy metals. An in vitro test of Solubility Bioaccessibility Research Consortium method (SBRC) and a modified sequential extraction method recommended by the European Community Bureau of Reference (BCR) were used to determine heavy metals bioaccessibility. The average bioaccessibility index (K) of most heavy metals was above 0.2, excluding Ba and Cr. In particular, extremely high bioaccessibilities of Zn (K = 0.83), Cd (K = 0.74), Pb (K = 0.62), and Cu (K = 0.59) were observed in the park dusts. Based on the Pb isotope technique, coal dust, soil parent materials and fertilizers, and traffic sources were accounting for 58%, 35%, and 7% of Pb in the park dust, respectively. The principle component analysis and multiple linear regression (PCA-MLR) results of the additive log-ratio transformation (coal combustion: 56.6%; soil parent materials and fertilizers: 36.8%; traffic sources: 6.6%) were more in good agreement with the Pb isotope technique results. Compared with the original data and the direct logarithmic transformation, the contributions were all positive values in the results of the additive log-ratio transformation, suggesting an effective method to open geochemical component data. Thus, the additive log-ratio transformation has strong interpretability in source appointment as well as better dimension reduction. This study provides an example to explore bioaccessibility in view of binding state and identify sources of multiple heavy metals in the park dust using properly transformed data in conjunction with Pb isotopes technique.

Urban soil contamination in Salerno (Italy): Concentrations and patterns of major, minor, trace and ultra-trace elements in soils

This work discusses the results of a geochemical survey conducted in the Salerno urban area to determine the sources patterns of major, minor, trace and ultra-trace elements in soils. In particular, the study focused on elements that are potentially toxic and listed in the environmental Italian legislation (D.L. 152/06), in order to effectively monitoring an important aspect of environment health. A total of 151 topsoil samples were collected, air-dried and sieved (<2 mm). After aqua regia digestion the samples were analyzed for 42 elements by ICP-MS and ICP-AES. Geostatistical analyses were carried out in order to show the single element spatial distribution and the distribution of factor scores elemental associations from R-mode factor analysis. In performing factor analysis, the additive logratio (alr) transformation was applied to the whole dataset in order to deal with the closure effects of the investigated geochemical data, avoiding artefacts and spurious correlation. The use of alr-transformed data instead of the normal data in the factor analysis allowed for a better interpretation of the distribution patterns, since this produced four factor models which, once mapped, were easier to interpret.The study revealed that major and minor elements (Al, Ca, Fe, K, Mg, Na, P, S and Ti) have a perfectly natural distribution with no discernible association to any human activity or presence. In contrast, many trace and ultra-trace elements (Ag, As, Au, Ba, Be, Cd, Co, Cr, Cu, Hg, Mn, Mo, Ni, Pb, Pd, Pt, Rh, Sb, Sn, Tl, V and Zn) show anomalous concentration values located almost exclusively in highly inhabited areas, industrial sites and along high traffic roads. Other trace and ultra-trace elements (B, Bi, Ga, La, Sc, Se, Sr, Te, Th, Tl, U and W) show concentrations compatible with the natural background levels. Some potentially toxic elements (e.g. Pb and Zn) reach concentration levels tens of times higher than the legal limits in the busiest areas of the city. Exposure to high concentrations of these contaminants may cause health problems to people living in these zones.

Comparison of additive and isometric log-ratio transformations combined with machine learning and regression kriging models for mapping soil particle size fractions

Digital soil mapping approaches relating to the soil particle size fractions (psf) face the challenge around how to establish the statistical or geostatistical models from large sets of environmental variables, especially in a situation with sparse soil profile data. Recently, many machine learning (ML) models have sprung up with advantages over statistical models. However, few studies focused on the comprehensive comparative analyses between ML and geostatistical models in the soil psf mapping. And the exploration of optimal combination of data transformation and model simulation was even less. Therefore, two transformed methods such as additive log-ratio (ALR) and isometric log-ratio (ILR) transformations combine with two ML models such as boosted regression tree (BRT), random forest (RF) and a classic geostatistical model of regression kriging (RK) were implemented to map soil psf in the Heihe River basin, China. A total of 640 samples and thirteen scorpan factors were collected and used for the comprehensive comparative analysis. Results showed that the scorpan factors such as temperature, precipitation, elevation, soil type, soil organic carbon, vegetation types and normalized difference vegetation index had important impacts on the soil psf mapping. ILR transformation was better than ALR transformation with advantage of improving stability of data distributions and ML models could also improve the mapping performance in comparison with RK models for better handling candidate factors. For these ML models, the RF models had better accuracy performance than the BRT models. In contrast, ILR transformation combined with RF model (ILR_RF) had the best performance, with the lowest root mean square error values (sand, 15.35%; silt, 14.20%; and clay, 6.66%), Aitchison distance value (0.86), standardized residual sum of squares value (0.60), and the highest concordance correlation coefficient value (0.73) and coefficient of determination value (56.69%) for clay content. In addition, ILR_RF had a relatively higher right ratio of soil texture type (68.44%) and better predict performance for most soil texture types. The predicted maps generated from ILR_RF presented more reasonable and smoother transitions. In the future, more ML models should be explored and more variables related to soil psf should be introduced into the models to improve the predictive performance.

Co-simulated Size Number: An Elegant Novel Algorithm for Identification of Multivariate Geochemical Anomalies

Identification of geochemical anomalies is of particular importance for tracing the footprints of anomalies. This can be implemented by advanced techniques of exploratory data analysis, such as fractal/multi-fractal approaches based on priori or posteriori distribution of geochemical elements. The latter workflow involves analysis of 2D/3D produced maps, which can be mostly obtained by geostatistical algorithms. There are two challenging issues for such an analysis. The first one corresponds to handling the cross-correlation structures among the data, and the second one relates to the compositional nature of data. To tackle these problems, this paper investigates the application of Gaussian co-simulation for modeling the cross-correlated compositional data in order to recognize the multivariate geochemical anomalies in integration with fractal analysis. In this context, an innovative algorithm, namely co-simulated size number (CoSS-N), is introduced for this purpose. The compositional nature of data is addressed by additive log-ratio transformation of original data while the Gaussian co-simulation handles the reproduction of cross-correlation among the components. The co-simulated outputs are then taken into account for capturing different geochemical populations, showing different levels of backgrounds and anomalies. The algorithm is illustrated via a real case study located in Philippine wherever seven geochemical components are required to be considered. The accuracy of results is examined by statistical validation techniques, indicating the capability of the CoSS-N algorithm for multivariate identification of geochemical anomalies.

Predicting regional spatial distribution of soil texture in floodplains using remote sensing data: A case of southeastern Iran

Soil texture is a physical property of soil and knowledge on its spatial distribution is essential for many agricultural and environmental activities especially in alluvial plains. This study aimed to predict the spatial distribution of soil fractions (i.e. percentages of sand, silt, and clay) in Sistan floodplain on a regional scale (area: 1500 km2). Random forest (RF), regression kriging-neural network residual kriging (RKNNRK), neural network residual kriging (NNRK), regression kriging (RK), and cokriging (COK) methods were used to map soil texture components over the region. Soil fractions were measured for 160 soil samples taken from the surface layer (0–30 cm) of various soil series in agriculture land of Sistan floodplain. The additive log-ratio (alr) transformation was applied to transform texture components prior to prediction. Remote sensing data including Landsat 8′ Bands (1–8), Band 4 to Band 8 ratio, Band 4 to Band 3 ratio, NDVI, GSI, Brightness Index, and Clay Index were used as auxiliary variables for interpolation of soil fractions. 80% of actual data was used for prediction and 20% of data was used for validation. The performance of methods used was evaluated using RMSE, ME and MAE criteria. The results showed that the RKNNRK model has the highest accuracy for prediction of sand (RMSE = 15.04%) and clay (RMSE = 8.77%) contents while the most accurate model for predicting silt content is NNRK (RMSE = 12.68%). RK and COK performed worse than NNRK and RKNNRK. A relatively high value of RMSE obtained for sand (17.89%), silt (14.15%), and clay (8.89%) contents by the RF model. This could be due to the low relief of study area, regional scale effects, low density of sampling points and high heterogeneity of soil texture components in floodplains. Our findings revealed that RKNNRK and NNRK models, when combined with remote sensing data, produce more accurate results and therefore can be used for appropriate mapping of soil fractions in floodplains and on a regional scale.

Multi-element comparisons of tapes evidence using dimensionality reduction for calculating likelihood ratios

Computing the likelihood ratio (LR), as a measure of weight of evidence, has traditionally been difficult for multi-element evidence. A solution based on multivariate random effects models has been adopted by the forensic community but suffers from instability and has a tendency toward extreme values. This problem is magnified by increasing the number of variables. In this study, we consider reducing the dimensionality of the problem using principal component analysis (PCA) and a post-hoc calibration step suggested by van Es et al. [1] and evaluate the performance of this method using multi-element data collected from electrical tapes with up to 18 elements measured. A set of 90 tapes known to originate from different sources were analyzed by LA-ICP-MS. We used additive log-ratio transformation with respect to the signal of 208Pb to transform the 18-dimensional data. This transformation altered the scale of the signals and more importantly, the transformed signals exhibited characteristics similar to a normal distribution. We used scores of the first five principal components (PCs) as input to the LR formula given by Aitken and Lucy [2] where we assumed multivariate normal between-sources distribution (LR MVN) to compare the tapes.We observed that the calculated LRs were extremely positive and negative and did not conform with the definition of well-calibrated LRs. Thus, we used the post-hoc calibration method given by van Es et al. [1] to calibrate the likelihood ratios. The calibrated LRs were obtained within an appropriate range.Five scenarios, each related to the number of principal components used to compare the samples formed part of this study. The first scenario made the comparisons using only the first PC, the second scenario used the first two PCs together and so on. The last scenario, LR5, used 5 PCs for the comparisons. Comparing the results of these 5 scenarios provided an understanding around sensitivity of the method based on the percentage of information used for the comparisons.The lowest false exclusion (Type I) and false inclusion (Type II) error rates were obtained for LR5 scenario in comparison to all the other scenarios. False inclusion and false exclusion error rates of 3.7% and 2.2% were reported by using only 5 out of 17 PCs. False exclusion error rates of 2.2% indicated that only two same-source comparisons had LR<1.The proposed method overcomes the problem of using highly-dimensional data for the comparisons, while using a high percentage of information present in the original data.

The iBox-FC: A new containment vessel for Itrax X-ray fluorescence core-scanning of freeze cores

A combination of Itrax micro-X-ray fluorescence core scanning (μXRF-CS) and freeze coring can facilitate the development of high-resolution (e.g. sub-decadal) paleoclimate records in lacustrine systems where low sedimentation rates and poorly consolidated “colloidal soup” at the sediment/water interface prevents retrieval and Itrax-μXRF-CS analysis of undisturbed cores using conventional gravity corers. The iBox-FC containment vessel described and tested here delays thawing of highly perishable freeze cores for up to two hours, providing adequate time to carry out high-resolution Itrax-μXRF-CS analysis. The iBox-FC is comprised of an open-topped Styrofoam box divided into chambers using high-density polyethylene (HDPE) that are filled with freeze pack gel. When the vessel is frozen, core slabs up to 13 cm long may be positioned into a central chamber and then scanned following normal Itrax-μXRF-CS methodology. To test the reliability of μXRF-CS analysis obtained from frozen sediments, a freeze core recovered from Control Lake, Northwest Territories, Canada, was sub-sectioned and analyzed using μXRF-CS and then subsampled for ICP-MS following near-total acid digestion. Comparison of μXRF-CS and ICP-MS results showed strong correlations (R2 > 0.8) for six of nine elements calibrated, and moderate correlations (R2 > 0.3) for the remaining three. Additive log-ratio transformation of data minimized specimen, matrix and edge effects associated with the high porewater contents of the freeze cores and slight melting of the sediment during analysis. These analytical effects had more impact on the lower concentration elements (As, Zn, Ni, Cu) than the higher concentration elements (Ti, K, Mn, Fe, Ca).

Comparison of soil texture maps synthetized from standard depth layers with directly compiled products

There are increasing demands nowadays on spatial soil information in order to support environmental related and land use management decisions. Physical soil properties, especially particle size distribution play important role in this context. A few of the requirements can be satisfied by the sand-, silt-, and clay content maps compiled according to global standards such as GlobalSoilMap (GSM) or Soil Grids. Soil texture classes (e. g. according to USDA classification) can be derived from these three fraction data, in this way texture map can be compiled based on the proper separate maps.Soil texture class as well as fraction information represent direct input of crop-, meteorological- and hydrological models. The model inputs frequently require maps representing topsoil features, which refer most commonly to 0–30 cm depth. This is covered by three consecutive depth intervals according to standard specifications: 0–5 cm, 5–15 cm, 15–30 cm. Becoming GSM and SoilGrids the most detailed freely available spatial soil data sources, the common model users (e. g. meteorologists, agronomists, or hydrologists) would produce input map from (the thickness-weighted mean of) these three layers. However, if the basic soil data and proper knowledge is obtainable, a soil texture map targeting directly the 0–30 cm layer could be independently compiled.In our work we compared Hungary's soil texture maps compiled using the same reference and auxiliary data and inference methods but for differing layer distribution. We produced the 0–30 cm clay, silt and sand map as well as the maps for the three standard layers (0–5 cm, 5–15 cm, 15–30 cm). Maps of sand-, silt-, and clay content were computed through composite regression kriging applying Additive Log-Ratio (alr) transformation. In addition to the Hungarian Soil Information and Monitoring System as reference soil data, digital elevation model and its derived components, soil physical property maps, remotely sensed images, land use-, geological-, as well as meteorological data were applied as auxiliary variables.We compared the directly compiled and the synthetized clay-, sand content, and texture class maps by different tools. In addition to pairwise comparison of basic statistical features (histograms, scatter plots), we examined the spatial distribution of the differences. We quantified the taxonomical distances of the textural classes, in order to investigate the differences of the map-pairs.We concluded that the directly computed and the synthetized maps show various differences. In the case of clay-, and sand content maps, the map-pairs have to be considered statistically different. On the other hand, the differences of the texture class maps are not significant. However, in all cases, the differences rather concern the extreme ranges and categories. Using of synthetized maps can intensify extremities by error propagation in models and scenarios. Based on our results, we suggest the usage of the directly composed maps.

Compositional time series analysis for Air Pollution Index data

The increasing importance of understanding the structure of Air Pollution Index (API) makes it necessary to come out with a compositional of API based on its pollutants. This will be more comprehensible for the public and easier to cooperate with authorities in reducing the causes of air pollution. Since five pollutants contribute in determining the API values, API can be shown as a compositional data. This study is conducted based on the data of API and its pollutants collected from Klang city in Malaysia for the period of January 2005 to December 2014. The proportion of each pollutant in API is considered as a component with five components in a compositional API. The existence of zero components in some pollutants, that have no effect on API, is a serious problem that prevents the application of log-ratio transformation. Thus, the approach of amalgamation has been used to combine the components with zero in order to reduce the number of zeros. Also, a multiplicative replacement has been utilized to eliminate the zero components and replace them with a small value that maintains the ratios of nonzero components. Transforming the compositional data to log-ratio coordinates has been done using the additive log ratio transformation, and the transformed series is then modeled by using a VAR model. Four criteria are used to determine the number of lags p of VAR(p) and these are: the Akaike Information, the Schwartz, the Hannan–Quinn and the Final Prediction Error criteria. Based on the results, A VAR (1) model with no constants or trend is considered as the best fitted model and it is used to forecast 12 months ahead. In addition, API values are mainly determined by PM10 that has a proportion close to one most of the time during study period. Therefore, authorities and researchers need to study the sources of PM10 and provide the public with useful information and alternatives in term of reducing the air pollution.

Application of cluster analysis to geochemical compositional data for identifying ore-related geochemical anomalies

Cluster analysis is a well-known technique that is used to analyze various types of data. In this study, cluster analysis is applied to geochemical data that describe 1444 stream sediment samples collected in northwestern Xinjiang with a sample spacing of approximately 2 km. Three algorithms (the hierarchical, k-means, and fuzzy c-means algorithms) and six data transformation methods (the z-score standardization, ZST; the logarithmic transformation, LT; the additive log-ratio transformation, ALT; the centered log-ratio transformation, CLT; the isometric log-ratio transformation, ILT; and no transformation, NT) are compared in terms of their effects on the cluster analysis of the geochemical compositional data. The study shows that, on the one hand, the ZST does not affect the results of column- or variable-based (R-type) cluster analysis, whereas the other methods, including the LT, the ALT, and the CLT, have substantial effects on the results. On the other hand, the results of the row- or observation-based (Q-type) cluster analysis obtained from the geochemical data after applying NT and the ZST are relatively poor. However, we derive some improved results from the geochemical data after applying the CLT, the ILT, the LT, and the ALT. Moreover, the k-means and fuzzy c-means clustering algorithms are more reliable than the hierarchical algorithm when they are used to cluster the geochemical data. We apply cluster analysis to the geochemical data to explore for Au deposits within the study area, and we obtain a good correlation between the results retrieved by combining the CLT or the ILT with the k-means or fuzzy c-means algorithms and the potential zones of Au mineralization. Therefore, we suggest that the combination of the CLT or the ILT with the k-means or fuzzy c-means algorithms is an effective tool to identify potential zones of mineralization from geochemical data.

Mapping the reliability of the additive log-ratio transformation

Data for which ratios of parts are more important than absolute values have a compositional nature and should be analysed in the (D - 1)-dimensional simplex, but in order to use standard multivariate analysis techniques they are often mapped bijectively from the simplex into the ordinary Euclidean space. The additive log-ratio (alr) is one popular ad hoc transformation, that has already been shown to amplify the relative errors in data, in some cases by an unbounded factor. In this paper an explicit mapping of the reliability of the alr transformed data is derived, given the desired accuracy and the relative error of the sensors acquiring them. To this purpose, first the relative condition number for the alr transformation has been defined and plotted in the 3-simplex, then a generalised characterisation of well conditioned compositions (with a condition number less than or equal to an arbitrary threshold) has been derived and finally isoconditioning surfaces have been defined, analytically derived and plotted in the 3-simplex.

Mapping the reliability of the additive log-ratio transformation

Data for which ratios of parts are more important than absolute values have a compositional nature and should be analysed in the (D - 1)-dimensional simplex, but in order to use standard multivariate analysis techniques they are often mapped bijectively from the simplex into the ordinary Euclidean space. The additive log-ratio (alr) is one popular ad hoc transformation, that has already been shown to amplify the relative errors in data, in some cases by an unbounded factor. In this paper an explicit mapping of the reliability of the alr transformed data is derived, given the desired accuracy and the relative error of the sensors acquiring them. To this purpose, first the relative condition number for the alr transformation has been defined and plotted in the 3-simplex, then a generalised characterisation of well conditioned compositions (with a condition number less than or equal to an arbitrary threshold) has been derived and finally isoconditioning surfaces have been defined, analytically derived and plotted in the 3-simplex.