Monitoring procedures in environmental geochemistry and compositional data analysis theory

First discussion on compositional data analysis is attributable to Karl Pearson, in 1897. However, notwithstanding the recent developments on algebraic structure of the simplex, more than twenty years after Aitchison’s idea of log-transformations of closed data, scientific literature is again full of statistical treatments of this type of data by using traditional methodologies. This is particularly true in environmental geochemistry where besides the problem of the closure, the spatial structure (dependence) of the data have to be considered. In this work we propose the use of log-contrast values, obtained by a simplicial principal component analysis, as LQGLFDWRUV of given environmental conditions. The investigation of the log-constrast frequency distributions allows pointing out the statistical laws able to generate the values and to govern their variability. The changes, if compared, for example, with the mean values of the random variables assumed as models, or other reference parameters, allow defining monitors to be used to assess the extent of possible environmental contamination. Case study on running and ground waters from Chiavenna Valley (Northern Italy) by using Na+, K+, Ca2+, Mg2+, HCO3-, SO4 2- and Cl- concentrations will be illustrated

New insights on river water chemistry by using non-centred simplicial principal component analysis: a case study

The use of perturbation and power transformation operations permits the investigation of linear processes in the simplex as in a vectorial space. When the investigated geochemical processes can be constrained by the use of well-known starting point, the eigenvectors of the covariance matrix of a non-centred principal component analysis allow to model compositional changes compared with a reference point. The results obtained for the chemistry of water collected in River Arno (central-northern Italy) have open new perspectives for considering relative changes of the analysed variables and to hypothesise the relative effect of different acting physical-chemical processes, thus posing the basis for a quantitative modelling

Thermodynamics and log–contrast analysis in fluid geochemistry

There are two principal chemical concepts that are important for studying the natural environment. The first one is thermodynamics, which describes whether a system is at equilibrium or can spontaneously change by chemical reactions. The second main concept is how fast chemical reactions (kinetics or rate of chemical change) take place whenever they start. In this work we examine a natural system in which both thermodynamics and kinetic factors are important in determining the abundance of NH+4 , NO−2 and NO−3 in superficial waters. Samples were collected in the Arno Basin (Tuscany, Italy), a system in which natural and antrophic effects both contribute to highly modify the chemical composition of water. Thermodynamical modelling based on the reduction-oxidation reactions involving the passage NH+4 -> NO−2 -> NO−3 in equilibrium conditions has allowed to determine the Eh redox potential values able to characterise the state of each sample and, consequently, of the fluid environment from which it was drawn. Just as pH expresses the concentration of H+ in solution, redox potential is used to express the tendency of an environment to receive or supply electrons. In this context, oxic environments, as those of river systems, are said to have a high redox potential because O2 is available as an electron acceptor. Principles of thermodynamics and chemical kinetics allow to obtain a model that often does not completely describe the reality of natural systems. Chemical reactions may indeed fail to achieve equilibrium because the products escape from the site of the rection or because reactions involving the trasformation are very slow, so that non-equilibrium conditions exist for long periods. Moreover, reaction rates can be sensitive to poorly understood catalytic effects or to surface effects, while variables as concentration (a large number of chemical species can coexist and interact concurrently), temperature and pressure can have large gradients in natural systems. By taking into account this, data of 91 water samples have been modelled by using statistical methodologies for compositional data. The application of log–contrast analysis has allowed to obtain statistical parameters to be correlated with the calculated Eh values. In this way, natural conditions in which chemical equilibrium is hypothesised, as well as underlying fast reactions, are compared with those described by a stochastic approach

L' ensenyament de l' estadística dels 11 als 16 anys

Publicació dirigida als docents que recull els continguts i els aspectes metodològics per a l' ensenyament de l'estadística en el nivell educatiu d' ESO i Batxillerat. També conté un resum comentat de les 27 unitats didàctiques que configuren la segona part de l' Estadística en el vostre món

L' estadística en el vostre món : llibre del professor 1

L' Estadística en el vostre món consta de 27 unitats didàctiques dirigides als alumnes, independents unes de les altres, i estructurades en quatre nivells de dificultat, de l'1 al 4. Cada unitat consta del material per l'alumne i del material pel docent. El material pel docent conté un recull exhaustiu d'orientacions adreçades als professors pel desenvolupament de la unitat a l' aula i amb les solucions dels exercicis proposats als alumnes. Aquest correspon al material pel docent de la unitat didàctica amb nivell de dificultat 1

L' estadística en el vostre món : llibre del professor 2

L' Estadística en el vostre món consta de 27 unitats didàctiques dirigides als alumnes, independents unes de les altres, i estructurades en quatre nivells de dificultat, de l'1 al 4. Cada unitat consta del material per l'alumne i del material pel docent. El material pel docent conté un recull exhaustiu d'orientacions adreçades als professors pel desenvolupament de la unitat a l' aula i amb les solucions dels exercicis proposats als alumnes. Aquest correspon al material pel docent de la unitat didàctica amb nivell de dificultat 2

L' estadística en el vostre món : llibre del professor 3

L' Estadística en el vostre món consta de 27 unitats didàctiques dirigides als alumnes, independents unes de les altres, i estructurades en quatre nivells de dificultat, de l'1 al 4. Cada unitat consta del material per l'alumne i del material pel docent. El material pel docent conté un recull exhaustiu d'orientacions adreçades als professors pel desenvolupament de la unitat a l' aula i amb les solucions dels exercicis proposats als alumnes. Aquest correspon al material pel docent de la unitat didàctica amb nivell de dificultat 3

L' estadística en el vostre món : llibre del professor 4

L' Estadística en el vostre món consta de 27 unitats didàctiques dirigides als alumnes, independents unes de les altres, i estructurades en quatre nivells de dificultat, de l'1 al 4. Cada unitat consta del material per l'alumne i del material pel docent. El material pel docent conté un recull exhaustiu d'orientacions adreçades als professors pel desenvolupament de la unitat a l' aula i amb les solucions dels exercicis proposats als alumnes. Aquest correspon al material pel docent de la unitat didàctica amb nivell de dificultat 4

L' estadística en el vostre món : [llibre de l'alumne] 1

L' Estadística en el vostre món consta de 27 unitats didàctiques dirigides als alumnes i estructurades en quatre nivells de dificultat, de l'1 al 4. Cada unitat consta del material per l'alumne i del material pel docent. Aquest correspon al material per l'alumne de la unitat didàctica amb nivell de dificultat 1

L' estadística en el vostre món : [llibre de l'alumne] 2

L' Estadística en el vostre món consta de 27 unitats didàctiques dirigides als alumnes i estructurades en quatre nivells de dificultat, de l'1 al 4. Cada unitat consta del material per l'alumne i del material pel docent. Aquest correspon al material per l'alumne de la unitat didàctica amb nivell de dificultat 2

L' estadística en el vostre món : [llibre de l'alumne] 3

L' Estadística en el vostre món consta de 27 unitats didàctiques dirigides als alumnes i estructurades en quatre nivells de dificultat, de l'1 al 4. Cada unitat consta del material per l'alumne i del material pel docent. Aquest correspon al material per l'alumne de la unitat didàctica amb nivell de dificultat 3

L' estadística en el vostre món : [llibre de l'alumne] 4

L' Estadística en el vostre món consta de 27 unitats didàctiques dirigides als alumnes i estructurades en quatre nivells de dificultat, de l'1 al 4. Cada unitat consta del material per l'alumne i del material pel docent. Aquest correspon al material per l'alumne de la unitat didàctica amb nivell de dificultat 4

Atmospheric downwelling longwave radiation at the surface during cloudless and overcast conditions. Measurements and modeling

Atmospheric downwelling longwave radiation is an important component of the terrestrial energy budget; since it is strongly related with the greenhouse effect, it remarkably affects the climate. In this study, I evaluate the estimation of the downwelling longwave irradiance at the terrestrial surface for cloudless and overcast conditions using a one-dimensional radiative transfer model (RTM), specifically the Santa Barbara DISORT Atmospheric Radiative Transfer (SBDART). The calculations performed by using this model were compared with pyrgeometer measurements at three different European places: Girona (NE of the Iberian Peninsula), Payerne (in the East of Switzerland), and Heselbach (in the Black Forest, Germany). Several studies of sensitivity based on the radiative transfer model have shown that special attention on the input of temperature and water content profiles must be held for cloudless sky conditions; for overcast conditions, similar sensitivity studies have shown that, besides the atmospheric profiles, the cloud base height is very relevant, at least for optically thick clouds. Also, the estimation of DLR in places where radiosoundings are not available is explored, either by using the atmospheric profiles spatially interpolated from the gridded analysis data provided by European Centre of Medium-Range Weather Forecast (ECMWF), or by applying a real radiosounding of a nearby site. Calculations have been compared with measurements at all sites. During cloudless sky conditions, when radiosoundings were available, calculations show differences with measurements of -2.7 ± 3.4 Wm-2 (Payerne). While no in situ radiosoundings are available, differences between modeling and measurements were about 0.3 ± 9.4 Wm-2 (Girona). During overcast sky conditions, when in situ radiosoundings and cloud properties (derived from an algorithm that uses spectral infrared and microwave ground based measurements) were available (Black Forest), calculations show differences with measurements of -0.28 ± 2.52 Wm2. When using atmospheric profiles from the ECMWF and fixed values of liquid water path and droplet effective radius (Girona) calculations show differences with measurements of 4.0 ± 2.5 Wm2. For all analyzed sky conditions, it has been confirmed that estimations from radiative transfer modeling are remarkably better than those obtained by simple parameterizations of atmospheric emissivity.