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

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

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