On the use of combined compact scheme for numerical solution of the two-layer oceanic shallow water equations

Many types of oceanic physical phenomena have a wide range in both space and time. In general, simplified models, such as shallow water model, are used to describe these oceanic motions. The shallow water equations are widely applied in various oceanic and atmospheric extents. By using the two-layer shallow water equations, the stratification effects can be considered too. In this research, the sixth-order combined compact method is investigated and numerically implemented as a high-order method to solve the two-layer shallow water equations. The second-order centered, fourth-order compact and sixth-order super compact finite difference methods are also used to spatial differencing of the equations. The first part of the present work is devoted to accuracy assessment of the sixth-order super compact finite difference method (SCFDM) and the sixth-order combined compact finite difference method (CCFDM) for spatial differencing of the linearized two-layer shallow water equations on the Arakawa's A-E and Randall's Z numerical grids. Two general discrete dispersion relations on different numerical grids, for inertia-gravity and Rossby waves, are derived. These general relations can be used for evaluation of the performance of any desired numerical scheme. For both inertia-gravity and Rossby waves, minimum error generally occurs on Z grid using either the sixth-order SCFDM or CCFDM methods. For the Randall's Z grid, the sixth-order CCFDM exhibits a substantial improvement , for the frequency of the barotropic and baroclinic modes of the linear inertia-gravity waves of the two layer shallow water model, over the sixth-order SCFDM. For the Rossby waves, the sixth-order SCFDM shows improvement, for the barotropic and baroclinic modes, over the sixth-order CCFDM method except on Arakawa's C grid. In the second part of the present work, the sixth-order CCFDM method is used to solve the one-layer and two-layer shallow water equations in their nonlinear form. In one-layer model with periodic boundaries, the performance of the methods for mass conservation is compared. The results show high accuracy of the sixth-order CCFDM method to simulate a complex flow field. Furthermore, to evaluate the performance of the method in a non-periodic domain the sixth-order CCFDM is applied to spatial differencing of vorticity-divergence-mass representation of one-layer shallow water equations to solve a wind-driven current problem with no-slip boundary conditions. The results show good agreement with published works. Finally, the performance of different schemes for spatial differencing of two-layer shallow water equations on Z grid with periodic boundaries is investigated. Results illustrate the high accuracy of combined compact method.

Validation of back-calculation equations for juvenile bluefish (Pomatomus saltatrix) with the use of tetracycline-marked otoliths

In recent years, a decrease in the abundance of bluefish (Pomatomus saltatrix) has been observed (Fahay et al., 1999; Munch and Conover, 2000) that has led to increased interest in a better understanding the life history of the species. Estimates of several young-of-the-year (YOY) life history characteristics, including the importance and use of estuaries as nursery habitat (Kendall and Walford, 1979) and size-dependant mortality (Hare and Cowen, 1997), are reliant upon the accuracy of growth determination. By using otoliths, it is possible to use back-calculation formulae (BCFs) to estimate the length at certain ages and stages of development for many species of fishes. Use of otoliths to estimate growth in this way can provide the same information as long-term laboratory experiments and tagging studies without the time and expense of rearing or recapturing fish. The difficulty in using otoliths in this way lies in validating that 1) there is constancy in the periodicity of the increment formation, and 2) there is no uncoupling of the relationship between somatic and otolith growth. To date there are no validation studies demonstrating the relationship between otolith growth and somatic growth for bluefish. Daily increment formation in otoliths has been documented for larval (Hare and Cowen, 1994) and juvenile bluefish (Nyman and Conover, 1988). Hare and Cowen (1995) found ageindependent variability in the ratio of otolith size to body length in early age bluefish, although these differences varied between ontogenetic stages. Furthermore, there have been no studies where an evaluation of back-calculation methods has been combined with a validation of otolithderived lengths for juvenile bluefish.

A reassessment of equations for predicting natural mortality in Mediterranean teleosts

This brief article presents new empirical models for prediction of natural mortality (M) from growth parameters (L and K, W and K) in Mediterranean teleosts, based on 56 data sets presented in an earlier paper in the January 1993 issue of Naga, the ICLARM Quarterly in which models were presented that included temperature as a predictor variable, although its effect was nonsignificant and its partial slope had the "wrong" sign.

Empirical equations for the estimation of natural mortality in Mediterranean teleosts

Empirical relationships were established linking estimates of the instantaneous rate of natural mortality (M), the von Bertalanffy growth parameters, L sub( infinity ) (or W sub( infinity )) and K, and annual mean water temperature in 56 stocks of Mediterranean teleosts fish. It is suggested that these relationships generate for these fish more reliable estimates of M than the widely-used model of Pauly (1980, J. Cons. CIEM 33(3):175-192), which was based on 175 fish stocks, but included only five stocks from the Mediterranean.

Length-weight relationship of marine fishes from southern Brazil

The relationship between length (L) and weight (W) was estimated for 80 species belonging to 50 families of marine fishes from the shelf and upper slope of southern Brazil (lat. 28°S - 34°S). Sample sizes (n) for different species ranged from 11 to 14 741 specimens collected from commercial landings and research surveys. The fit of the equations (W=aLb) with a and b parameters estimated from regular and functional regression (of log-transformed weight and length data) as well as from a non-linear iterative process using the quasi-Newton algorithm were compared. The non-linear method gave the most accurate estimates in terms of residual sum of squares. Differences were less than 2.3% for n>500 compared with predictive regressions and 1.5% compared with functional regressions. No difference was observed between both predictive and functional regressions. Determination coefficients (r2) increased with sample size, and the highest r2 were obtained for 50

Beverton and Holt equations: spreadsheet functions and uncertainty

This contribution illustrates how modern spreadsheets aid the calculation and visualization of yield models and how the effects of uncertainties may be incorporated using Monte Carlo simulation. It is argued that analogous approaches can be implemented for other assessment models of simple to medium complexity justifying wider use of spreadsheets in fisheries analysis and training.

An environmentally based growth model that uses finite difference calculus with maximum likelihood method: its application to the brackish water bivalve Corbicula japonica in Lake Abashiri, Japan

We present a growth analysis model that combines large amounts of environmental data with limited amounts of biological data and apply it to Corbicula japonica. The model uses the maximum-likelihood method with the Akaike information criterion, which provides an objective criterion for model selection. An adequate distribution for describing a single cohort is selected from available probability density functions, which are expressed by location and scale parameters. Daily relative increase rates of the location parameter are expressed by a multivariate logistic function with environmental factors for each day and categorical variables indicating animal ages as independent variables. Daily relative increase rates of the scale parameter are expressed by an equation describing the relationship with the daily relative increase rate of the location parameter. Corbicula japonica grows to a modal shell length of 0.7 mm during the first year in Lake Abashiri. Compared with the attain-able maximum size of about 30 mm, the growth of juveniles is extremely slow because their growth is less susceptible to environmental factors until the second winter. The extremely slow growth in Lake Abashiri could be a geographical genetic variation within C. japonica.

Age and growth of the estuarine dolphin (Sotalia guianensis) (Cetacea, Delphinidae) on the Paraná Coast, southern Brazil

Teeth of 71 estuarine dolphins (Sotalia guianensis) incidentally caught on the coast of Paraná State, southern Brazil, were used to estimate age. The oldest male and female dolphins were 29 and 30 years, respectively. The mean distance from the neonatal line to the end of the first growth layer group (GLG) was 622.4 ±19.1 μm (n=48). One or two accessory layers were observed between the neonatal line and the end of the first GLG. One of the accessory layers, which was not always present, was located at a mean of 248.9 ±32.6 μm (n=25) from the neonatal line, and its interpretation remains uncertain.The other layer, located at a mean of 419.6 ±44.6 μm (n=54) from the neonatal line, was always present and was first observed between 6.7 and 10.3 months of age. This accessory layer could be a record of weaning in this dolphin. Although no differences in age estimates were observed between teeth sectioned in the anterior-posterior and buccal-lingual planes, we recommend sectioning the teeth in the buccal-lingual plane in order to obtain on-center sections more easily. We also recommend not using teeth from the most anterior part of the mandibles for age estimation. The number of GLGs counted in those teeth was 50% less than the number of GLGs counted in the teeth from the median part of the mandible of the same animal. Although no significant difference (P>0.05) was found between the total lengths of adult male and female estuarine dolphins, we observed that males exhibited a second growth spurt around five years of age. This growth spurt would require that separate growth curves be calculated for the sexes. The asymptotic length (TL∞), k, and t0 obtained by the von Bertalanffy growth model were 177.3 cm, 0.66, and –1.23, respectively, for females and 159.6 cm, 2.02, and –0.38, respectively, for males up to five years, and 186.4 cm, 0.53 and –1.40, respectively, for males older than five years. The total weight (TW)/total length (TL) equations obtained for male and female estuarine dolphins were TW = 3.156 × 10−6 × TL 3.2836 (r=0.96), and TW = 8.974 × 10−5 × TL 2.6182 (r=0.95), respectively.

Determination of length-weight relationship in Sepia pharaonis and test for sex specific variation

The parameters a and b of the length-weight relationship of Sepia pharaonis of the form of W=a.L was determined. Sex separated size fequency data collected from Karachi fish Harbour was analysed the length-weight equations, separable by male, female and sex combined. The apparent difference in paired values of exponents b1, b2 for any combination i.e. male versus female and male, female versus sex combined was tested for their significant difference. No significant difference was observed for any combination, this indicated no sex specific variation in length-weigh relationship of Sepia pharaonis.

Study on some biological and feeding factors of spined loach Cobitis taenia from the Babolrud, Talar and Siahrud Rivers

Spined loach, Cobitis taenia, is a predominant fish in the river systems of the southern Caspian Sea basin. Although there is evidence of the geographical divergence of this taxon, but no information is available on morphological differences within the species populations. This study was designed to evaluate some biological factors including; morphometric and meristic characters, length-weight, age-growth, condition factor, diet, reproduction, variation and differentiation, in the Babolrud, Talar and Siahrud Rivers in south of the Caspian Sea basin. Age, sex ratio, fecundity, ova diameter and gonadosomatic index were estimated. Also, regression analyses was tested the relation between fecundity and fish length, weight, gonad weight, and also age. Totally 858 fish of which 721 were matures, were collected from these rivers by electrofishing. 37 morphometric characters, 9 meristic characters and 78 truss network system characters were estimated. Resulats of DFA analysis based on data of morphometric and meristic showd that these populations are highly (94.5%) varios from each other. In discriminate function analysis, the proportion of individuals correctly classified into their original groups was 61%, 65.4% and 86.5% for upstream and downstream, respectively. Clustering based on Euclidean distances among groups of centroids using an UPGMA and also principal component analysis’ results for morphometric data indicated that these populations from these three rivers were clearly distinct from each other. Regression equations between length and weight in these three populations were significantly different from Folton factor (b=3), that showed the fish has a negative Alometric growth process. Condition factor was estimated between 0.8912 to 1.2736 and 0.8131 to 1.4489 for males and females, respectively. Sex ratio (female: male) in these populations was 1.2816:1. The difference between the number of females and males was significant and females were more than males. The female and male specimens reach maturity by Tl more than 40 and 30 mm and at the age of 2+ and 1+, respectively. The mean of ova diameter was 0.5824±0.2882. The spawning took place from May to late July, at the water temperature from 18.7 to 24.0°C. The GSI values average at the beginning of the reproduction period was about 9%, with ranged from 2 to 26% in ripe mature females. The absolute and relative fecundity were 2109±792 and 579±208 respectively. The absolute fecundity was significantly related to body weight and gonads weight. Based on the pattern of gonado-somatic index, it was concluded that this fish has prolong active reproductive period, which is a type of adaptation by short-lived small fishes to environmental conditions. The macroscopic and histological results showed that the female and male have 5 and 4 stages in their maturation process, respectively. The RLG index was about 0.4732, which showed the fish is a carnivorous species. Significant difference was observed between fishes with different length and diet. The main foods of the fish were Trichoptera, Chironomidae larvae and Ephemeroptera which were their prefered food as well, however it was estimated that the food selection and diet are affected by environmental conditions.

Survey of plankton blooms and red tides and their interaction with environmental factors through monitoring satellite images

One of the most important marine ecological phenomena is red tide which is created by increasing of phytoplankton population, influenced by different factors such as climate condition changes, utrification hydrological factors and can leave sever and undesired ecological and economical effects behind itself in the case of durability. Coast line of Hormozgan is about 900km from east to west, within the range of geographical coordinates of 56 16 23.8, 26 58 8.8 to 54 34 5.33 and 26 34 32 eastern longitude and northern latitude, seven sampling stations were considered and sampled for a period of one year from October 2008 to October 2009. after the analysis of Satellite images, monthly, during the best time. In several stages, samplings were performed. In each station, three samples were collected for identification and determination of Bloom- creating species abundance. Cochlodinium polykrikoides was the species responsible for the discoloration which occurred at October 2008 in Hormozgan marine water. Environmental parameters such as sea surface temperature, pH, salinity, Dissolved Oxygen concentration, Total Dissolved Solids (T.D.S.), conductivity, nitrate, nitrite and phosphate and also chlorophyll a were measured and calculated. Kruscal Wallis test was used to compare the densities between different months, seasons and the studied stations. Mann-whitney test from Nonparametric Tests was used for couple comparison. Pearson correlation coefficient was used to determine the relationship between physical and chemical data set and the abundance of Cochlodinium polykrikoides. Multivariate Regression and analysis of variance (ANOVA) also were used to obtain the models and equations of red tide occurrence relationship, environmental parameters and nutrient data. The highest density was 26 million cells per liter in Qeshm station. A meaningful difference was observed between sampling months and seasons but there was no between sampling stations which indicates that in favorable conditions, the occurrence of this phenomenon by the studied species is probable. Regarding to β coefficients of nitrate, temperature, phosphate, Total Dissolvable Solutions (T.D.S) and pH these parameters are effective on the abundance of this species and red tide occurrence. Increase in these factors can represent the effects and outcomes of human activities and increase in marine pollution.

Morphometric and meristic studies of the spotted estuarine prawn, Macrobrachium equidens (Dana) of Vembanad Lake, Kerala State

The paper reports on the statistical analysis of growth pattern and meristic studies of body parts of the spotted estuarine prawn, Macrobrachium equidens (Dana) of Vembanad Lake, Kerala State. The results showed that the growth pattern of carapace length, telson length, ischium length and dactylus length in relation to total length were significantly different between the sexes at slope itself (at 1% level) and growth pattern of abdominal length, merus length, carpus length, propodus length and palm length were significant at elevations (5%, 1% levels). The average sizes of all these characters were greater in males than in females. Regression equations have been calculated for the characters and presented in the text. Among the characters of the carapace, rostrum length, post-orbital length showed significant difference between sexes at 1% level (slope value) and width of carapace at 1% level (elevations). The average sizes of all these characters were higher in males. Among the meristic characters studied, the species exhibited sexual dimorphism with regard to dorsal teeth, post-orbital teeth and ventral teeth. The fundamental data generated is essential for establishing the species status as well as it is useful for making comparison with other species.