Statistical treatment of grain-size curves and empirical distributions: densities as compositions?

The preceding two editions of CoDaWork included talks on the possible consideration of densities as infinite compositions: Egozcue and D´ıaz-Barrero (2003) extended the Euclidean structure of the simplex to a Hilbert space structure of the set of densities within a bounded interval, and van den Boogaart (2005) generalized this to the set of densities bounded by an arbitrary reference density. From the many variations of the Hilbert structures available, we work with three cases. For bounded variables, a basis derived from Legendre polynomials is used. For variables with a lower bound, we standardize them with respect to an exponential distribution and express their densities as coordinates in a basis derived from Laguerre polynomials. Finally, for unbounded variables, a normal distribution is used as reference, and coordinates are obtained with respect to a Hermite-polynomials-based basis. To get the coordinates, several approaches can be considered. A numerical accuracy problem occurs if one estimates the coordinates directly by using discretized scalar products. Thus we propose to use a weighted linear regression approach, where all k- order polynomials are used as predictand variables and weights are proportional to the reference density. Finally, for the case of 2-order Hermite polinomials (normal reference) and 1-order Laguerre polinomials (exponential), one can also derive the coordinates from their relationships to the classical mean and variance. Apart of these theoretical issues, this contribution focuses on the application of this theory to two main problems in sedimentary geology: the comparison of several grain size distributions, and the comparison among different rocks of the empirical distribution of a property measured on a batch of individual grains from the same rock or sediment, like their composition

INFO2009 Group 16 - The Rice Box Resources

INFO2009, Coursework 2, Green ICT/IT

The release of silicon from amorphous silica and rice straw in Sri Lankan soils

Silicon release from rice straw and amorphous silica when shaken in solution with five Sri Lankan soils was studied indirectly using sorption isotherms and changes in concentration and directly using straw in dialysis bags examined using electron microscopy. The aim was to further our understanding of the processes and factors affecting the release of straw-Si in soils and its availability to rice. The soils (alfisols and ultisols) shaken with 0.1 M NaCl (5 g per 125 mL for 250 days) produced concentrations of 1 - 4 mg L-1 of monosilicic acid-Si. Amorphous silica added to these suspensions (36.5 mg, containing 17 mg Si) raised the concentrations to 20 - 40 mg L-1, and added rice straw (0.5 g, containing 17 mg Si) gave 10 - 25 mg L-1. Sorption isotherms (7 days equilibrations) were used to calculate from the concentrations the amounts of Si released ( 24 - 38% and 8 - 21%, respectively). Both materials gave about 40 mg L-1 of monosilicic acid-Si plus 30 mg L-1 of disilicic acid-Si when shaken in solution alone (5 g per 125 mL). Straw in dialysis bags ( 0.5 g per 25 mL in 0.1 M NaCl) was shaken in soil suspension ( 5 g per 100 mL) for 60 days. Similar concentrations and releases were measured to those obtained above. About one fifth of the mass of straw was lost by decomposition in the first 15 days. A chloroform treatment prevented decomposition, but Si release was unaffected. Disintegration continued throughout the experiments, with phytoliths being exposed and dissolved. Compared to the rate of release from straw into solution without soil, the release of Si into soil suspensions was increased during the first 20 days by adsorption on the soil, but was then reduced probably through the effect of Fe and Al on the phytolith surfaces. The extent of this blocking effect varied between soils and was not simply related to soil pH.

Utilisation by upland rice of plant residue- and fertiliser-phosphorus in two tropical acid soils

A dual isotopic technique was used to assess the effects of soil type, and residues of Gliricidia sepium, without and with added fertiliser-P on the utilisation of P. Upland rice (Oryza sativa) was grown for 70 days in two tropical acid soils of different P sorbing capacity and P status. Uniformly P-32-labelled soils were treated with inorganic fertiliser-P tagged with P-33, Gliricidia sepium residue applied at planting and 3 weeks earlier, and in a combination of fertiliser-P and Gliricidia applied at and 3 weeks before planting. There were significant responses of shoot and root weights, and total P uptake to Gliricidia- and/or fertiliser-P addition in the Ultisol (low P status) but not the Oxisol (high P status), suggesting that P in the latter soil was not yield limiting, despite the high standard P requirement. Similarly, incorporation of Gliricidia three weeks before planting further increased shoot weight only in the Ultisol. There were generally higher proportions, quantities and percent utilisations of the Gliricidia- P and fertiliser-P in the Ultisol than in the Oxisol. Gliricidia significantly increased the utilisation of fertiliser-P only in the Ultisol. However, early application of Gliricidia increased Gliricidia- P but not fertiliser-P utilisation in the Ultisol. Added fertiliser-P did not influence Gliricidia- P utilisation.

Does reactive surface area depend on grain size? Results from pH 3, 25 circle C far-from-equilibrium flow-through dissolution experiments on anorthite and biotite

Laboratory determined mineral weathering rates need to be normalised to allow their extrapolation to natural systems. The principle normalisation terms used in the literature are mass, and geometric- and BET specific surface area (SSA). The purpose of this study was to determine how dissolution rates normalised to these terms vary with grain size. Different size fractions of anorthite and biotite ranging from 180-150 to 20-10 mu m were dissolved in pH 3, HCl at 25 degrees C in flow through reactors under far from equilibrium conditions. Steady state dissolution rates after 5376 h (anorthite) and 4992 h (biotite) were calculated from Si concentrations and were normalised to initial- and final- mass and geometric-, geometric edge- (biotite), and BET SSA. For anorthite, rates normalised to initial- and final-BET SSA ranged from 0.33 to 2.77 X 10(-10) mol(feldspar) m(-2) s(-1), rates normalised to initial- and final-geometric SSA ranged from 5.74 to 8.88 X 10(-10) mol(feldspar) m(-2) s(-1) and rates normalised to initial- and final-mass ranged from 0.11 to 1.65 mol(feldspar) g(-1) s(-1). For biotite, rates normalised to initial- and final-BET SSA ranged from 1.02 to 2.03 X 10(-12) mol(biotite) m(-2) s(-1), rates normalised to initial- and final-geometric SSA ranged from 3.26 to 16.21 X 10(-12) mol(biotite) m(-2) s(-1), rates normalised to initial- and final-geometric edge SSA ranged from 59.46 to 111.32 x 10(-12) mol(biotite) m(-2) s(-1) and rates normalised to initial- and final-mass ranged from 0.81 to 6.93 X 10(-12) mol(biotite) g(-1) s(-1). For all normalising terms rates varied significantly (p <= 0.05) with grain size. The normalising terms which gave least variation in dissolution rate between grain sizes for anorthite were initial BET SSA and initial- and final-geometric SSA. This is consistent with: (1) dissolution being dominated by the slower dissolving but area dominant non-etched surfaces of the grains and, (2) the walls of etch pits and other dissolution features being relatively unreactive. These steady state normalised dissolution rates are likely to be constant with time. Normalisation to final BET SSA did not give constant ratios across grain size due to a non-uniform distribution of dissolution features. After dissolution coarser grains had a greater density of dissolution features with BET-measurable but unreactive wall surface area than the finer grains. The normalising term which gave the least variation in dissolution rates between grain sizes for biotite was initial BET SSA. Initial- and final-geometric edge SSA and final BET SSA gave the next least varied rates. The basal surfaces dissolved sufficiently rapidly to influence bulk dissolution rate and prevent geometric edge SSA normalised dissolution rates showing the least variation. Simple modelling indicated that biotite grain edges dissolved 71-132 times faster than basal surfaces. In this experiment, initial BET SSA best integrated the different areas and reactivities of the edge and basal surfaces of biotite. Steady state dissolution rates are likely to vary with time as dissolution alters the ratio of edge to basal surface area. Therefore they would be more properly termed pseudo-steady state rates, only appearing constant because the time period over which they were measured (1512 h) was less than the time period over wich they would change significantly. (c) 2006 Elsevier Inc. All rights reserved.

Effects of manure and fertilizer on grain yield, soil carbon and phosphorus in a 13-year field trial in semi-arid Kenya

Long-term indicators of soil fertility were assessed by measuring grain yield, soil organic carbon (SOC) and soil Olsen phosphorous for a P-deficient soil. In one set of treatments, goat manure was applied annually for 13 years at 0, 5 and 10 t ha(-1), and intercrops of sorghum/cowpea, millet/green gram and maize/pigeonpea were grown. Yield depended on rainfall and trends with time were not identifiable. Manure caused an upward trend in SOC, but 10 t ha(-1) manure did not give significantly more SOC than 5 t ha(-1). Only 10 t ha(-1) manure increased Olsen P. Measurements of both SOC and Olsen P are recommended. In another set of treatments, manure was applied for four years; the residual effect lasted another seven to eight years when assessed by yield, SOC and Olsen P Treatment with mineral fertilizers provided the same rates of N and P as 5 t hat manure and yields from manure and fertilizer were similar. Fertilizer increased Olsen P but not SOC. Management systems with occasional manure application and intermediate fertilizer applications should be assessed. Inputs and offtakes of C, N and P were measured for three years. Approximately 16, 25 and 11% of C, N and P respectively were stabilized into soil organic matter from 5 t ha(-1) a(-1) manure. The majority of organic P was fixed as soil inorganic P.