A comparison of two methods for developing the linearization of a shallow-water model

We develop the linearization of a semi-implicit semi-Lagrangian model of the one-dimensional shallow-water equations using two different methods. The usual tangent linear model, formed by linearizing the discrete nonlinear model, is compared with a model formed by first linearizing the continuous nonlinear equations and then discretizing. Both models are shown to perform equally well for finite perturbations. However, the asymptotic behaviour of the two models differs as the perturbation size is reduced. This leads to difficulties in showing that the models are correctly coded using the standard tests. To overcome this difficulty we propose a new method for testing linear models, which we demonstrate both theoretically and numerically. © Crown copyright, 2003. Royal Meteorological Society

Flux comparison of Eulerian and Lagrangian estimates of Agulhas leakage: A case study using a numerical model

Estimating the magnitude of Agulhas leakage, the volume flux of water from the Indian to the Atlantic Ocean, is difficult because of the presence of other circulation systems in the Agulhas region. Indian Ocean water in the Atlantic Ocean is vigorously mixed and diluted in the Cape Basin. Eulerian integration methods, where the velocity field perpendicular to a section is integrated to yield a flux, have to be calibrated so that only the flux by Agulhas leakage is sampled. Two Eulerian methods for estimating the magnitude of Agulhas leakage are tested within a high-resolution two-way nested model with the goal to devise a mooring-based measurement strategy. At the GoodHope line, a section halfway through the Cape Basin, the integrated velocity perpendicular to that line is compared to the magnitude of Agulhas leakage as determined from the transport carried by numerical Lagrangian floats. In the first method, integration is limited to the flux of water warmer and more saline than specific threshold values. These threshold values are determined by maximizing the correlation with the float-determined time series. By using the threshold values, approximately half of the leakage can directly be measured. The total amount of Agulhas leakage can be estimated using a linear regression, within a 90% confidence band of 12 Sv. In the second method, a subregion of the GoodHope line is sought so that integration over that subregion yields an Eulerian flux as close to the float-determined leakage as possible. It appears that when integration is limited within the model to the upper 300 m of the water column within 900 km of the African coast the time series have the smallest root-mean-square difference. This method yields a root-mean-square error of only 5.2 Sv but the 90% confidence band of the estimate is 20 Sv. It is concluded that the optimum thermohaline threshold method leads to more accurate estimates even though the directly measured transport is a factor of two lower than the actual magnitude of Agulhas leakage in this model.

Edible oil from Tiger nut (Cyperus esculentus L.): mechanical pressing and aqueous enzymatic extraction methods

The tiger nut tuber of the Cyperus esculentus L. plant is an unusual storage system with similar amounts of starch and lipid. The extraction of its oil employing both mechanical pressing and aqueous enzymatic extraction (AEE) methods was investigated and an examination of the resulting products was carried out. The effects of particle size and moisture content of the tuber on the yield of tiger nut oil with pressing were initially studied. Smaller particles were found to enhance oil yields while a range of moisture content was observed to favour higher oil yields. When samples were first subjected to high pressures up to 700 MPa before pressing at 38 MPa there was no increase in the oil yields. Ground samples incubated with a mixture of α- Amylase, Alcalase, and Viscozyme (a mixture of cell wall degrading enzyme) as a pre-treatment, increased oil yield by pressing and 90% of oil was recovered as a result. When aqueous enzymatic extraction was carried out on ground samples, the use of α- Amylase, Alcalase, and Celluclast independently improved extraction oil yields compared to oil extraction without enzymes by 34.5, 23.4 and 14.7% respectively. A mixture of the three enzymes further augmented the oil yield and different operational factors were individually studied for their effects on the process. These include time, total mixed enzyme concentration, linear agitation speed, and solid-liquid ratio. The largest oil yields were obtained with a solid-liquid ratio of 1:6, mixed enzyme concentration of 1% (w/w) and 6 h incubation time although the longer time allowed for the formation of an emulsion. Using stationary samples during incubation surprisingly gave the highest oil yields, and this was observed to be as a result of gravity separation occurring during agitation. Furthermore, the use of high pressure processing up to 300 MPa as a pre-treatment enhanced oil yields but additional pressure increments had a detrimental effect. The quality of oils recovered from both mechanical and aqueous enzymatic extraction based on the percentage free fatty acid (% FFA) and peroxide values (PV) all reflected the good stabilities of the oils with the highest % FFA of 1.8 and PV of 1.7. The fatty acid profiles of all oils also remained unchanged. The level of tocopherols in oils were enhanced with both enzyme aided pressing (EAP) and high pressure processing before AEE. Analysis on the residual meals revealed DP 3 and DP 4 oligosaccharides present in EAP samples but these would require further assessment on their identity and quality.