Optimum Sample Size to Detect Perturbation Effects: The Importance of Statistical Power Analysis – A Critique

Abstract. The current article describes statistical power analysis as an efficient strategy for the estimation of the optimum sample size. The principle aim is constructively to criticise and enrich the results presented by Mouillot et al. (1999) , who estimate the optimum sample size for evaluating possible perturbations. The authors did not make any reference to statistical power analysis, even though their objective clearly went beyond a simple stock evaluation to assess management strategies in a particular marine ecosystem. Surprisingly, they proposed (a priori) an ANOVA design to test a hypothesis considering both space and temporal scales. However, the authors did not cover important topics related with power analysis and the precautionary principle, both used into environment impact assessment programmes for marine ecosystems. Based on their results and on statistical power analysis, it is demonstrated that the variability (dispersion statistics), a key factor they used to estimate the sample size, is less relevant than the magnitude of perturbation (effect size). Therefore, a greater effort must be devoted to estimate the effect size of a particular phenomenon rather than a desired variability.     

Surface circulation of the Levantine Basin: Comparison of model results with observations

The eastern Mediterranean (Levantine Basin) hydrography and circulation are investigated by comparing the results of a high-resolution primitive equation model with observations. After a 10-year integration, the model is able to reproduce the major water masses and the circulation patterns of the eastern Mediterranean. Comparisons with the POEM hydrographical observations show good agreement. The vertical distribution of the water masses matches that of the observations quite well in terms of monthly mean. The model surface circulation is in agreement with circulation schemes derived from recent observations. Some well-known mesoscale features of the upper thermocline circulation are also realistically reproduced. In agreement with satellite observations, the model shows that high-energy mesoscale eddies dominate the upper thermocline circulation in the southern and the central parts of the Levantine Basin. Most of the Atlantic Water follows the north African coast and forms a strong coastal jet near the Libyan coast rather than forming the Mid-Mediterranean Jet described by several authors. The sub-basin circulation shows a strong seasonal signal. A strong and stable current flows along the isobaths in winter, becoming weaker and with more meanders in summer. The mesoscale eddies throughout the whole basin are more energetic in summer than in winter.     

Baroclinic Buoyancy-Inertia Joint Stability Parameter

At present, the barotropic buoyant stability parameter has been derived from a vertical virtual displacement of a water parcel. The barotropic inertial stability parameter in the eccentrically cyclogeostrophic, basic current field was derived in 2003 from a horizontal cross-stream virtual displacement of a parcel. By expressing acceleration of a parcel due to a virtual displacement, which is arbitrarily sloping within a vertical section across the basic current, in terms of natural coordinates, we derived the vertical component of baroclinic buoyant stability parameter B ₂ ², the horizontal component of baroclinic inertial stability parameter I ₂ ², the baroclinic joint stability parameter J ², its buoyant component B ² and its inertial component I ². B ² is far greater than I ₂ ², and when neglecting relative vorticity except for vertical shear, a downward convex curve of J ² plotted against the slope of a virtual displacement follows a trend of B ² curve. If a parcel displaces along a horizontal surface or an isopycnal surface, however, B ² vanishes, and J ² becomes equal to I ². Actual parcel is apt to displace not only along the bottom slope, but also along the sea surface and an isopycnal interfacial surface, which is approximately equivalent to an isentropic surface, preferred by lateral mixing and exchange of momentum. Such actual displacement makes B ² vanishing, and grants I ² an important role. The present analysis of I ² examining effects due to curvature and horizontal and vertical shear vorticities are useful in deepening our understanding of baroclinic instability in actual oceanic streams.     

Shoreline variability via empirical orthogonal function analysis: Part I temporal and spatial characteristics

Empirical orthogonal functions (EOFs) or principal components were used to extract the significant modes of shoreline variability from several data sets collected at three very different locations. Although EOFs have proven to be a valuable tool in the analysis of nearshore data, most applications have focused on the ability of the technique to describe cross-shore or profile variability. Here however, EOFs were used to help identify the dominant modes of longshore shoreline variability at Duck, North Carolina, the Gold Coast, Australia, and at several locations within the Columbia River Littoral Cell in the U.S. Pacific Northwest. In part one of this analysis, characteristic patterns of shoreline variability identified by the EOF analysis are described in detail. At each site, the dominant modes consisting of the first four eigenfunctions were found to describe nearly 95% of the total shoreline variability. At both Duck and the Gold Coast, several interesting longshore periodic features suggestive of sand waves were identified, while boundary effects related to natural headlands and navigational structures/entrances dominated the Pacific Northwest data sets.     

波群作用于垂直桩柱的峰力统计性质

研究具有窄谱和Ｗｅｉｂｕｌｌ波高分布的波群对非线性桩柱系统作用力的统计性质。求得了桩桩的波浪峰力的各种特征值及其比值。指出这些数值不仅是阻力一惯性力参数ｂＨ的函数，也随着波群因子而变化。本文模式更具广泛性。文中给出了一系列计算图表，可从理论计算波群作用于桩柱的波浪峰力。     

Water mass formation variability in the intermediate layer of the east sea

Long-term variability in the intermediate layer of the eastern Japan Basin has been investigated to understand the variability of water mass formation in the East Sea. The simultaneous decrease of temperature at shallower depths and oxygen increasing at deeper depths in the intermediate layer took place in the late 1960’s and the mid-1980’s. Records of winter sea surface temperatures and air temperatures showed that there were cold winters that persisted for several years during those periods. Therefore, it was assumed that a large amount of newly-formed water was supplied to the intermediate layer during those cold winters. Close analysis suggests that the formation of the Upper Portion of Proper Water occurred in the late 1960’s and the Central Water in the mid-1980’s.     

ASM1中污水水质参数与化学计量系数的估测

简要介绍了活性污泥1号模型中14个污水水质参数与5个化学计量系数的估测方法和典型取值。     

中国近海沿岸海温多时间尺度变率及影响其变化的天气气候因素

本文通过对中国近海13个海洋站1959年～2003年逐日日平均海表温度及其相关数据的处理分析,结合中国近海多年逐日天气实况,研究了中国近海水温的短时（1d）、过程、旬、月、年际变率以及海温的长期趋势变化,并在此基础上详细讨论了影响中国近海各时间尺度水温变化的天气气候因素.     

Sediment movement under unidirectional flows: an assessment of empirical threshold curves

A selection of threshold data sets from previous investigations is used to re-examine, selectively, some of the empirical curves that are most commonly used for the prediction of sediment threshold. Simple analytical formulae are derived describing single line curves for mean threshold values and envelopes for the initial movement of discrete particles and the commencement of mass sediment transport phases of the critical condition.The complexity of factors governing the prevailing conditions at threshold, together with the randomness of events, limits deterministic solutions; however, the curves provide an approach that can be used readily in practical applications. In contrast, the envelope presentation is more of a stochastic approach to the definition of threshold. It recognises that there is no definitive threshold condition under which a particular particle size can be displaced, but rather that a range of threshold values exist.The empirical threshold relationships were derived on the basis of a relatively large amount of data. However, the sources utilised have interpreted the ‘critical condition’ in various ways, implying that the formulae must be treated with caution in applications.