Problem statement: As a result of climate change more work is now being done on climate indices such as SOI, rainfall, temperature and so on. The research concerning rainfall and temperature variations in coastal tropical and subtropical catchments as noted by the dated references in this study shows a lack of attention. The authors examined long term data from coastal areas of Queensland. Australian climate is highly variable making the identification of trends or interactions between rainfall and temperature difficult to discern from background variation. Due to the lack of attention in the past, this study examined the relationships between rainfall, temperature, minimum temperature and maximum temperature as well as over time using time series methods. In particular, the study examined whether a cyclic nature existed in the data sets and whether a simple trend relationship between rainfall and temperature existed. To examine autocorrelation and seasonality ARIMA models were also investigated. Approach: A large data set involving more that 50 years of rainfall and temperature data were examined using spectral analysis, time series analysis-ARIMA methodology to analyse climatic trends and interactions. Fourier analysis, linear regression and ARIMA based time series models were used to analyze the large data sets using Matlab, SPSS and SAS programs. Results: The rainfall data was variable and appeared seasonal while the temperature data appeared stationary. Interestingly, spectral analysis showed variations in rainfall and temperature over 50-60 years but the results showed that rainfall and temperature varied coherently, with a cycle of about 2-3 years. An inverse relationship in trend was noted between rainfall and daily temperature range using linear regression among the variables. The ARIMA models showed autocorrelation and seasonality providing time series models. Conclusion/Recommendations: There is a cyclic pattern noted in both the rainfall and temperature time series and a cycle of about 3 years in the rainfall and temperature data sets suggesting a coherent variance in the relationship. This is an interesting finding suggesting a cyclic nature of large rainfall events over time and has been confirmed by the recent large rainfalls events in 2009-10. Linear regression showed an inverse relationship in trend between rainfall and temperature range only even though the r value was around 0.27. The autocorrelation in the data appears to have caused the low r and ARIMA methods was used giving time series models for each series allowing for autocorrelation and seasonality. This study on rainfall and temperature is valuable contribution to the lack of research noted particularly in Queensland as noted in the dated references found; also contributing to the climate change debate forcing it on the cautious side. Further work involving multivariate and dynamic conditional correlation methods may provide further insights regarding the relationships between rainfall and temperature. More climatic indices ...

This study focuses on students in first year environmental science degree programs where traditionally mathematical emphasis has been much less than the strict science or math majors. The importance now placed in applied mathematics means that students need to gain more conceptual and quantitative knowledge in not only the environmental degree programs but also in most if not all non-mathematical majors. In this study, the authors attempt to gain insights into why students fail in mathematical courses where the mathematical requirements are not as demanding as other strict math degree programs. This is done by examining student conceptual thinking patterns and strategies as evident in student prepared scripts. A total of 133 students were requested to prepare a focus sheet to summarize their knowledge on topics learned but they were also told that the focus sheets could be used in exams for notes. This motivated their sheet preparation. The students prepared weekly summaries and later revised and summarized them for later use. Detailed examination of such sheets allowed researchers to study students’ knowledge in terms procedural work, math skills, strategies and conceptual knowledge. A study of linear, quadratic and limit sections led to interesting insights not only regarding revision strategies, knowledge of content, but also conceptual and procedural knowledge base and higher order skills such as problem solving focus. Logical and creative competencies were assessed in terms of how and what student focused upon or linked to in order to facilitate application of knowledge. The results show average levels of procedural and conceptual competence but rather low levels in logical and creative competence in preparation of scripts. Almost 50% lacked competency in procedural work while around 54% lacked conceptual competency. Given the emphasis placed procedural skills by students, the levels were lower than expected. However, the lack of structure in their work and deeper levels of understanding of links between the topics learned was concerning. These findings have implications for the first year mathematics teaching teams at universities especially the non-specialist mathematical majors