Hybrid algorithms for cyclically reduced convection-diffusion problems

We consider hybrid and adaptive iterative algorithms for cyclically-reduced discrete convection-diffusion problems. Hybrid algorithms combine via a two phase algorithm, iterative methods which require no a priori information about the coefficient matrix in the first phase with Chebyshev or Richardson iteration in the second phase. For two-dimensional convection-diffusion problems, central difference discretization is considered and the resulting linear system is reduced to approximately half its size by applying one step of cyclic reduction. We examine the numerical performance of the hybrid methods for solving the reduced systems. Our numerical experiments show that for the class of problems considered, an adaptive Chebyshev algorithm that uses modified moments to approximate the eigenvalues requires less work in most cases than the hybrid algorithms based on GMRES/Richardson methods

Global Warming and Changing Temperature Patterns over Mauritius

This paper discusses the changing temperature pattern over Mauritius. We observe an increase of the annual mean temperature at Pamplemousses since 1876 with an average rate of 0.009oC per year with a significant correlation coefficient of 0.67. Compared to the mean temperature for the period of 1951 to 1960, we find that there is a shift in time (decadal) in the warming from northwest to other regions over the island. The temperature deviations are more marked in winter than in summer. Moreover, the number of hot days per year is increasing and the number of cold days is decreasing.Keywords: Temperature spatial variation, trend, hot and cold days, kriggin

Spatial distribution of surface chlorophyll a and micro-phytoplankton density and diversity around two islands and at two banks of the Mascarene region

The present study validated the use of AquaMODIS sea surface chlorophyll a (Chla) concentrations and investigated the spatial variation in density and diversity of micro-phytoplankton around two islands and two fishing banks of the Mascarene region. The study included areas around Mauritius (MRU) and Rodrigues (ROD) Islands, at Nazareth (NZ) Bank, and in the Joint Management Area (JMA) between the Republic of Mauritius and the Republic of Seychelles, more specifically at the Saya de Malha (SM) Bank. The AquaMODIS data were based on 67 match-up data points of in-situ against satellite Chla concentrations. The micro-phytoplankton community structure was investigated by determining the density variation and using the Shannon Wiener (H’) and Evenness (Evar) diversity indices. The satellite and in-situ Chla data were significantly and positively correlated when pooled for the four sites studied (R2 = 0.441; r = 0.642, P < 0.01), and when analysed separately for islands (R2 = 0.480; r = 0.694), and banks (R2 = 0.233; r = 0.483). However, the Chla satellite values tended to be lower than the in-situ Chla data. The highest densities of micro-phytoplankton were observed in the eastern and northern regions for MRU and ROD, respectively. The most dominant genera of micro-phytoplankton were Coscinodiscus, Navicula, Chaetoceros and Ceratium. The Shannon-Wiener diversity index values for diatoms were all above 2.5 with waters around the islands having higher diversity compared to the banks. Overall, the different micro-phytoplankton around the islands, except for the group of cyanobacteria at ROD Island, were more evenly distributed (Evar > 0.6) compared to the banks. This study indicated that AquaMODIS Chla satellite data is valid and may be potentially used as a proxy for in-situ Chla concentration on the Mascarene Plateau. The results of this study also provide detailed insight into the spatial variation in micro-phytoplankton density and diversity on the Mascarene Plateau in the Western Indian Ocean. Further long-term studies are warranted to thoroughly understand the temporal (including seasonal and inter-annual) variations in Chla and micro-phytoplankton distribution for adequate and appropriate management of these ocean territories

Variations in abundance, diversity, photo-physiology and estimated productivity of micro-phytoplankton with depth at the Saya de Malha Bank, Mascarene Plateau

The variations in micro-phytoplankton abundance, diversity, photo-physiology, chlorophyll a (Chla) concentration and estimated productivity were assessed at depth ranges of 0-4, 5-10, and 11-29 m with 100, 28 and 11% of irradiance, respectively, in Saya de Malha waters. The total micro-phytoplankton abundance (TMPA) differed significantly (P < 0.001) with depth ranges, and between day and night samples. Out of the 34 genera identified, 27 showed a decrease in abundance of over 40% with depth. Chaetoceros, Coscinodiscus, Navicula, Nitzschia and Ceratium were most dominant. The Shannon-Wiener (H’) diversity index did not differ among depth ranges and between samples collected during day and night, but diatoms were more diverse than dinoflagellates. The effective quantum yield (ΦPSII) and the light-use efficiency factor (α) tended to decrease, while the maximum relative electron transport rate (rETRmax), the photo-inhibitory factor (β) and the maximum non-photochemical quenching (NPQmax) varied insignificantly from morning to afternoon sampling points at all depth ranges studied. The estimated productivity, rETRmax and Chla concentration decreased with depth ranges. The higher diversity of diatoms, better photosynthetic performance in the morning hours and higher near-surface estimated productivity provide new insights into micro-phytoplankton dynamics and productivity in Saya de Malha waters

Using Learning Analytics to Investigate Student Performance in Blended Learning Courses

Many higher education institutions today offer online delivery as an alternative or addition to provide more flexibility to learners. However, students being confronted with such services come with different expectations to what that means to their learning paths and behaviours. Learning Analytics is a rather new and innovative way of making student behaviour and performances explicit through analysing large sets of learner data. In this article, we take the case of online and blended learning from the University of Mauritius and hold the analysis of student interaction data against their performances and achievements. The study encompasses the entire population of first year students over two consecutive academic years of an undergraduate programme in Web and Multimedia Development. We classified the data into distinctive parts namely participation (or engagement), coursework marks, exam marks, and overall results to identify relationships that may influence student retention. 29.03.2017 | Wolfgang Greller, Mohammad Issack Santally, Ravindra Boojhawon, Yousra Rajabalee & Roopesh Kevin Sungku

Temporal sensitivity analysis of erosivity estimations in a high rainfall tropical island environment

The Erosivity Index (EI) and the Modified Fournier Index (MFI) are two commonly used methods in calculating the R factor of the universal soil loss equation/ revised universal soil loss equation formula. Using Mauritius as a case study, the value of high-resolution data versus long-term totals in erosivity calculations is investigated. A limited number of four Mauritius Meteorological Services stations located on the west coast and the Central Plateau provided the study with detailed rainfall data for 6 years at 6-min intervals. Rainfall erosivity for erosive events was calculated using different set interval data. In this study, within the EI, the use of 6-min rainfall intervals during erosive rainfall gave estimates of around 10% more erosivity than the 30-min time intervals and 33% more rainfall erosivity than the 60-min rainfall measurements. When the MFI was used to determine erosivity through annual and monthly rainfall totals, substantially higher erosivity than the EI method was calculated in both regions. This stems from the large amount of non-erosive rainfall that is generated on Mauritius. Even when the MFI was used to calculate erosivity through monthly and annual rainfall totals derived purely from erosive rainfall, erosivity calculations were not comparable to those from high-resolution data within the EI. We suggest that for the computation of erosivity, rainfall data with the highest possible resolution should be utilised if available and that the application of annual and monthly rainfall totals to assess absolute soil erosion risk within a high rainfall tropical environment must be used with caution.http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1468-0459hb201

Intra-event characteristics of extreme erosive rainfall on Mauritius

Mauritius is a typical tropical volcanic island with a raised interior where extreme rainfall events generate the bulk of the erosivity. Intra-event characteristics of the 120 highest erosive events at six selected locations between 2004 and 2008 were analysed to provide the first detailed intra-storm data for a tropical island environment. On Mauritius, spatial variation is evident in the characteristics of the extreme erosive rainfall recorded at the stations, with a noticeable increase in rainfall depth, duration, kinetic energy and erosivity of extreme events with altitude. Extreme events in the raised interior (central plateau) show a high variability in peak intensity over time as well as a higher percentage of events with the greatest intensities in the latter part of the event. Intra-event distribution of rainfall in the interior of the island shows that rainfall has a higher potential to exceed infiltration rates as well as the ability to generate high peak runoff rates and substantial soil loss. The study suggests that even though the within-event rainfall characteristics is complex it has implications for soil erosion risk, and that in tropical island environments the within-storm distribution of rainfall must be incorporated in soil loss modelling.National Research Foundation (NRF)http://www.tandfonline.com/loi/tphy202017-05-31hb2016Geography, Geoinformatics and Meteorolog

The nature of erosive rainfall on a tropical volcanic island with an elevated interior

Mauritius is a typical tropical volcanic island with a distinct elevated central plateau above 550 m.a.s.l. Rainfall depth, duration, intensity, kinetic energy, and erosivity were analysed for 385 erosive rainfall events at five locations over a five-year period (2004 to 2008). Two Mauritius Meteorological Services stations located on the west coast and three sited on the Central Plateau provide detailed rainfall data at 6-minute intervals. Erosive storm events are found to differ markedly between the coastal lowlands and the elevated interior with regard to the frequency, the total rainfall generated, the duration, total kinetic energy, and total erosivity of individual events. However, mean kinetic energy, mean and maximum rainfall erosivity (EI30), and maximum intensities (I30) from individual erosive events do not show this distinct differentiation. The distribution of kinetic energy and erosivity generated by individual events at the two altitudes are also significantly different. Although erosivity measured during summer exceeds that recorded in winter, the data indicate that large percentages of winter rainfall events on Mauritius are erosive and rainfall from non-tropical cyclones can pose a substantial erosion risk. Soil erosion risk occurs from storm-scale to synoptic-scale events, and extreme rainfall events generate the bulk of the erosivity. This paper also highlights that the use of rainfall records at an event scale in soil erosion risk assessments on tropical islands with a complex topography increases the effectiveness of erosivity estimates.National Research Foundation (NRF).The Department of Geography, Geoinformatics, and Meteorology at the University of Pretoria and the Govan Mbeki Research and Development Centre at the University of Fort Hare supplied additional travel funding for WN, PS, RB, and TM.http://www.tandfonline.com/loi/tphy20hb201

GMRES implementations and residual smoothing techniques for solving ill-posed linear systems

AbstractThere are verities of useful Krylov subspace methods to solve nonsymmetric linear system of equations. GMRES is one of the best Krylov solvers with several different variants to solve large sparse linear systems. Any GMRES implementation has some advantages. As the solution of ill-posed problems are important. In this paper, some GMRES variants are discussed and applied to solve these kinds of problems. Residual smoothing techniques are efficient ways to accelerate the convergence speed of some iterative methods like CG variants. At the end of this paper, some residual smoothing techniques are applied for different GMRES methods to test the influence of these techniques on GMRES implementations

Rainfall-driven nutrient loading affects coastal phytoplankton in the southwestern Indian Ocean: a lagoon at Mauritius Island

This study aimed to test the effects of rainfall-driven nutrient loading on the microphytoplankton dynamics in the shallow water at Trou aux Biches  lagoon on the northwest coast of Mauritius. Changes in density, diversity and estimated productivity of microphytoplankton were monitored in  three zones—coast, lagoon and reef—during two rainfall periods of 4 and 3 days’ duration, respectively, in March–April 2017. The average nutrient  loading from terrestrial runoff was 15.5% and the salinity decreased by 2.5%. Following the two rainfall events, a 3-fold increase in total  microphytoplankton density (TMPD), with a dominance of diatoms, was noted within a week at the coast and lagoon, while it remained relatively  unchanged at the reef. These changes in microphytoplankton densities were concomitant with adequate levels of silicate (>2 μM) and high  nitrate:silicate ratios (2.84–6.93). During this study, the numbers of genera of diatoms, dinoflagellates and cyanobacteria observed were 28, 12 and  3, respectively. The Shannon–Wiener, equitability and evenness indices showed high diversity values for diatoms and cyanobacteria prior to the  rainfall events and for dinoflagellates after the events. The chlorophyll a content, relative electron transport rate, and estimated productivity of  microphytoplankton increased during and after the rainy periods. TMPD and chlorophyll a were correlated significantly and positively with  nutrients, salinity and temperature. Toxic algal species such as the dinoflagellates Alexandrium, Dinophysis and Tripos were recorded, although not  in bloom densities. These findings indicate that rainfall-driven nutrient loading led to an increase in microphytoplankton density and estimated  productivity, and a change in its diversity