Relationship between El Niño southern oscillation index and rainfall (Queensland, Australia)

This paper explores the relationship between El NiᯠSouthern Oscillation Index (SOI) and rainfall in South East Queensland. Several statistical models of the SOI and rainfall data are analysed including interactions. The results of the analyses show that although the SOI and rainfall can be predicted for short terms using time series analysis methods, mean squared error (MSE) and Theil's U showed that in comparison to persistence model forecasts may not be significantly better. Although the short term predictions may be worse, this does not mean that these cannot be used; rather, it shows that for different fitting and forecast periods, models can fail in predicting ahead. In fact weather forecasts can predict the short term rainfall well - but cannot predict monthly precipitation for two or three or more months ahead. In climate predictions the limit of predictability is reached when the standardised MSE reaches the climate variance (=1). All the rainfall models used in this study show an MSE well below 1, i.e. the models did not reach the limit of predictability.Griffith Sciences, Griffith School of EnvironmentFull Tex

Vedas and the Development of Arithmetic and Algebra

Problem statement: Algebra developed in three stages: rhetorical or prose algebra, syncopated or abbreviated algebra and symbolic algebra-known as "school algebra". School algebra developed rather early in India and the literature now suggests that the first civilization to develop symbolic algebra was the Vedic Indians. Approach: Philosophical ideas of the time influenced the development of the decimal system and arithmetic and that in turn led to algebra. Indeed, symbolic algebraic ideas are deep rooted in Vedic philosophy. The Vedic arithmetic and mathematics were of a high level at an early period and the Hindus used algebraic ideas to generate formulas simplifying calculations. Results: In the main, they developed formulas to understand the physical world satisfying the needs of religion (apara and para vidya). While geometrical focus, logic and proof type are features of Greek mathematics, "boldness of conception, abstraction, symbolism" are essentially in Indian mathematics. From such a history study, a number of implications can be drawn regarding the learning of algebra. Real life, imaginative and creative problems that encourage risk should be the focus in student learning; allowing students freely move between numbers, magnitudes and symbols rather than taking separate static or unchanging view. A move from concrete to pictorial to symbolic modes was present in ancient learning. Real life practical needs motivated the progress to symbolic algebra. The use of rich context based problems that stimulate and motivate students to raise levels higher to transfer knowledge should be the focus of learning. Conclusion/Recommendations: The progress from arithmetic to algebra in India was achieved through different modes of learning, risk taking, problem solving and higher order thinking all in line with current emphasis in mathematics education but at rather early stage in human history.Griffith Sciences, Griffith School of EnvironmentFull Tex

Changes in subsurface water quality during coastal canal state constructions

CHANGES IN SUBSURFACE WATER QUALITY DURING COASTAL CANAL ESTATE CONSTRUCTIONS Gurudeo A. Tularam1 and Julian Dobos2 1Lecturer and 2Postgraduate student, Faculty of Environmental Sciences, Griffith University, Brisbane Australia ABSTRACT Construction of coastal canal estates has increased in recent times in Australia. The lowering of the watertable is required during certain canal construction periods. Coastal low lands contain can contain pyrites and associated potential acid sulfate soils. Dewatering or lowering of the water table to allow for dry excavation, may permit oxidation of the pyritic soil causing acid generation. Saline intrusion may also occur via lowering of the watertable. A paucity of literature on coastal canal estates led to this study, which investigated the subsurface water quality during construction of a canal estate. Groundwater depth, pH, dissolved oxygen, titrated acidity and salinity were monitored on site at the Lake Kawana development in Queensland, Australia. Groundwater monitoring was carried out before, during and after the dewatering program. Data analysis showed that water depth increased during dewatering activities and decreased after re-flooding. The dissolved oxygen, titrated acidity and salinity levels rose during periods of increased groundwater depth, while pH levels fell. The increase in oxygen availability and the associated increase in acidity, may lead to dissolution of heavy metals, but monitoring data was lacking in this regard. Since salinity may increase due to other close by saline surface water bodies, further studies are required to understand subsurface flow patterns during dewatering operations. Computer simulation models could be developed to help determine the flow of contaminants during dewatering and re-flooding operations.Griffith Sciences, Griffith School of EnvironmentNo Full Tex

Number of Non-Unique Minors (of Various Orders) and Elements in the Calculation of General Determinants

Problem statement: Many distinct properties of determinants have been studied and are known, yet a considerable number of properties still need further examination. This study investigates the number of minors (of various orders) and elements of a matrix A contained in the expansion of the general determinant of A, irrespective of the independence, principality and distinctness of such minors and elements. Approach: A mathematical proof based approach is taken. Minors of all orders and elements in the calculations of general determinants of matrices of sizes 2䲬 3䳬 4䴍 and 5䵠respectively, are considered. Results: Two general expressions involving factorial terms are found: the first being equivalent to the number of minors of various orders found in the analysis of the considered matrices (mentioned above) and the second being equivalent to the number of elements found in the same analysis. Proofs are then presented showing that the expressions hold in the general case of a matrix of size n䮮 Conclusion: The results of this study present, with proof, expressions for the total number of minors (of various orders) and elements, respectively, in the general determinant of a matrix of size n䮬 irrespective of the independence, principality and distinctness of such minors and elements. Scope for further theoretical study, with applications in applied mathematics and the physical and computer sciences is also indicated.Arts, Education & Law Group, Queensland ConservatoriumFull Tex

Time series analysis of rainfall and temperature interactions in tropical catchments

see http://2008.appmath.ru/pub/49/program.pdfGriffith Sciences, Griffith School of EnvironmentNo Full Tex

Correction of errors in Vetschera's (2004) model of behavioral uncertainty and investment

Modelling of behavioural uncertainty has been a concern for researchers for some time. This paper briefly reviews modelling related to uncertainty and the focuses on the model presented by Vetschera (2004). A model of decision behaviour has been developed in the paper with regard to investment and cooperation taking into account the uncertainty and lack of information. The model is an important contribution for it focuses on situations that are not usual to the normal principle agent problems. The present review however reveals some errors in the paper. Sometimes errors may appear editorial but the same errors may lead the interested reader or researcher to inappropriate paths, particularly those who may fail to follow an argument or comprehend the underlying meanings of the equations and analytical solutions. In this manner, further work on this important topic may be hindered if researchers accept forms as presented in the paper literally as facts to further work. The main contribution of this paper is that it presents the correct forms of the mathematical aspects and procedures of the Vetschera (2004) paper.Griffith Sciences, Griffith School of EnvironmentNo Full Tex

Fishy tales: Behaviour of schooling fish escaping from terns

The aim of this study is to develop a better understanding of seabird foraging behaviour and the anti-predator behaviour of their prey. Studies of seabirds’ foraging and prey-capture behaviour, as it relates to the evasive and escape behaviour of schooling fish, are sparse. Our study was carried out at One Tree Reef on the southern end of the Great Barrier Reef, Australia. A school of hardyheads Pranesus capricornensis sheltered in the shallows over the sand flats in front of the research station for 14 non-consecutive days. In that time, Lesser Crested Terns Thalasseus bengalensis were observed for 10 hours from above the surface in 37 foraging bouts and for 40 minutes from underwater in at least one foraging bout. In each foraging bout, a single tern dived into the school. We found that terns on average dived at a rate of 0.67 ± 0.35 dives/minute from 4–5 m above the surface. The depth range of dives was 43–58 cm. Therefore, fish within 58 cm of the surface were potentially accessible. The total length of the hardyheads was 10–12 cm, which is within the size range useable by terns. Fish used flash expansion to escape diving terns and formed a vacuole around birds as they slowly ascended to the surface. This escape manoeuvre was effective about 80% of the time. The fish that were caught did not respond to the escape movements of the fish above them and, therefore, were isolated. Fish also used the C-startle response to escape terns underwater and in mid-air. The anti-predator manoeuvres of hardyheads are similar to those observed among Clupea spp. (herrings and sardines) and Ammodytes spp. (sand eels) escaping sub-surface predators. Hardyheads and sardines react in the same way to gannets Morus spp. and terns that plunge dive directly to their prey, partially confirming the prediction that results for plunge-diving gannets are generalisable to other gannets and boobies (Sula spp.), terns and gulls (Larus spp.), tropicbirds (Phaethon spp.), pelicans (Pelecanus spp.), and kingfishers (Alcedinidae).Full Tex

Water security problems in Asia and longer term implications for Australia

This paper reports on water security issues in Asia that has long-term security implications for Australia. Asia's water problems are severe with one in five people not having access to safe drinking water. Water security is defined as the availability of an acceptable quantity and quality of water for health, livelihoods, ecosystems and production, coupled with an acceptable level of water-related risks to people, environments and economies. It is a function of access to adequate quantities and acceptable quality, for human and environmental users. This analysis shows many Asian countries will face greater challenges than present from population explosion, shifts of populations from rural to urban areas, pollution of water resources and over-abstraction of groundwater. These challenges will be compounded by the effects of climate change over the next 50 years. It is then necessary to mobilise technologies, techniques, skills and research to aid security issues in Asia now. Otherwise, population growth, rapid urbanisation and climate change issues will worsen placing strong demands on water resources, thus creating water refugees, and this will affect countries close to Asia such as Australia. Reducing water's destructive potential and increasing its productive potential is a central challenge and goal for the sake of future generations in Asia and Australia.Griffith Sciences, Griffith School of EnvironmentNo Full Tex

Salinity intrusion in coastal drains and creeks

Griffith Sciences, Griffith School of EnvironmentNo Full Tex