Shoreline variability via empirical orthogonal function analysis: Part II relationship to nearshore conditions

The method of empirical orthogonal function (EOF) or principal component analysis (PCA) was used to investigate the spatial and temporal variability of shoreline data sets from Duck, North Carolina, the Gold Coast, Australia, and the United States Pacific Northwest. In the present work, an attempt is made to relate the individual modes of shoreline variability identified by the EOF analyses to select parameterizations of the nearshore environment. The parameters considered include the wave energy (E), the cross-shore and longshore wave energy fluxes (F_x and F_y), the wave steepness (H_o/L_o), the non-dimensional fall velocity parameter (Ω), the profile parameter (P), the surf-similarity parameter (ζ), and a surfzone Froude number (F_r). Correlation analyses were used to evaluate the linear relationship between each of these parameters and the temporal eigenfunctions, c_k(t), associated with individual modes of shoreline change. Typically, strong correlations were observed between longshore uniform modes and the monthly means of several of the nearshore parameters.     

Empirical orthogonal function analysis of shoreline changes behind two different designs of detached breakwaters

This paper compares the shoreline responses immediately shoreward of two adjacent schemes of segmented shore parallel rubble mound breakwaters undergoing the same forcing by waves and tides. Scheme one consists of four longer, emergent breakwaters that have produced tidal tombolos in their lee. Scheme two consists of five shorter, lower breakwaters that are submerged at higher tides with salients in the breakwater's lee. Empirical orthogonal function analysis was used to decompose a video derived shoreline dataset into the dominant modes of shoreline change for both schemes. The two schemes showed similar modes of change. The primary mode of change for both schemes was the cross-shore growth and shrinking of the salients/tombolos. The secondary mode of change was the longshore movement of the salients/tombolos. For all modes of change, the dominant length scale was dictated by the breakwater dimensions and locations. A new manifestation of hydrodynamic parameters is introduced: the cumulative integral of the de-meaned parameters. This parameterisation allowed for meaningful correlation of the temporal EOF components with forcing parameters and identification of the important influence of the tide on observed morphodynamic change. Clear differences were observed between the shoreline responses measured in schemes one and two; including differences in bay erosion/accretion; and the longshore translation of salients/tombolos. The beaches in scheme two showed behavioural patterns similar to unprotected beaches which were not observable in scheme one. It is postulated that these differences are caused both by the different breakwater designs and by variation in longshore sediment supply.     

Forecasting seasonal to multi-year shoreline change

This contribution details a simple empirical model for forecasting shoreline positions at seasonal to interannual time-scales. The one-dimensional (1-D) model is a simplification of a 2-D behavioural-template model proposed by Davidson and Turner (2009). The new model is calibrated and tested using five-years of weekly video-derived shoreline data from the Gold Coast, Australia. The modelling approach first utilises a least-squares methodology to calibrate the empirical model coefficients using the first half of the dataset of observed shoreline movement in response to known forcing by waves. The model is then verified by comparison of hindcast shoreline positions to the second half of the observed shoreline dataset. One thousand synthetic time-series of wave height and period are generated that encapsulate the statistical characteristics of the modelled wave field, retaining the observed seasonal variability and sequencing characteristics. The calibrated model is used in conjunction with the simulated wave time-series to perform Monte Carlo forecasting of the resulting shoreline positions. The ensemble-mean of the 1000 individual five-year shoreline simulations is compared to the unseen shoreline time-series. A simple linear trend forecast of the shoreline position was used as a baseline for assessing the performance of the model. The model performance relative to this baseline prediction was quantified by several objective methods, including cross-correlation (r), root mean square (RMS) error analysis and Brier Skill tests. Importantly, these tests involved no prior knowledge of either the wave forcing or shoreline response. The new forecast model was found to significantly improve shoreline predictions relative to the simple linear trend model, capturing well both the trend and seasonal shoreline variabilities observed at this site. Brier Skill Scores (BSS) indicate that the model forecasts based on unseen data were rated as ‘excellent’ (BSS = 0.83), and root mean square errors were less than 7 m (≈ 14% of the observed variability). The standard deviations of the 1000 individual simulations from ensemble-averaged ‘mean’ forecast were found to provide a useful means of predicting the higher-frequency (individual storm) shoreline variability, with 98% of the observed shoreline data falling within two standard deviations of the forecast position.     

Long-term shoreline response of a nontidal,barred coast

Long-term variations of shoreline positions along the southern Baltic coast were investigated using multichannel singular spectrum analysis (MSSA) to determine the most dominant long-term response patterns. The investigated beach is located at Lubiatowo on the Polish Coast and is mildly sloping with multiple bars. Data on coastal morphology have been collected at Lubiatowo including (1) bathymetric surveys since 1987 twice a year, and (2) beach topography surveys since 1983 every 4 weeks on the average, extending from the shoreline to the dune foot. Furthermore, several dedicated field campaigns have been carried out at Lubiatowo, as well as measurements of deep-water wave properties since 1998. MSSA was employed to the whole data set of shoreline position from all survey lines. In summary, three patterns emerged reproducing alongshore standing waves with different periods 7 to 8, 20+ and several decades. They represent long-term shoreline response, such that at some locations the longest wave is most predominant, at other locations the medium cycle predominates, whereas the shortest is the most prominent at yet other locations. However, all three can be detected at every location monitored, eliminating the confusion resulting from ordinary singular spectrum analysis (SSA) analysis, done previously for the same data set.     

Analysis of variations in the surface temperature of tropical and Northern Pacific Ocean

Studies on the analysis of the Pacific Ocean surface temperature are presented based on the data of the NCEP/NCAR reanalysis. Two methods are used in the work. The first is a classical analysis of the empirical orthogonal functions (EOFs) that makes it possible to identify the El Niño and La Niña phenomena in tropics. In this case, the anomalies of the ocean surface temperature (OST) are reconstructed during these events with quite high accuracy when using several first EOFs. In contrast, at the time between these events, more harmonics are required for the reconstruction. The OST variability in the middle and high latitudes cannot be identified highly accurately based on this approach, since it is considerably weaker than a strong signal in tropics. This signal was detected by the method of cluster analysis. The results show that, in addition to the signal in tropics, there are well-pronounced quasi-decadal signals between the eastern and western Pacific, as well as in the region of the Kuroshio continuation and in the subpolar gyre that can be identified with Pacific decadal oscillations (PDOs).     

Statistical analysis and forecasts of long-term sandbank evolution at Great Yarmouth, UK

A data-driven model has been developed to analyse the long-term evolution of a sandbank system and to make ensemble predictions in a period of 8 years. The method uses a combination of empirical orthogonal function (EOF) analysis, (to define spatial and temporal patterns of variability), jack-knife resampling, (to generate an ensemble of EOFs), a causal auto-regression technique, (to extrapolate the temporal eigenfunctions), and straightforward statistical analysis of the resulting ensemble of predictions to determine a ‘forecast’ and associated uncertainty. The methodology has been applied to a very demanding site which includes a curved shoreline and a group of mobile nearshore sandbanks. The site is on the eastern coast of the UK and includes the Great Yarmouth sandbanks and neighbouring shoreline. A sequence of 33 high quality historical survey charts reaching back to 1848 have been used to analyse the patterns and to predict morphological evolution of the sandbank system. The forecasts demonstrate an improved skill relative to an assumption of persistence, but suffer in locations where there are propagating features in the morphology that are not well-described by EOFs.     

A simple equilibrium model for predicting shoreline change

This contribution describes the development, calibration and verification of a 1-D behaviour-orientated shoreline prediction model. The model primarily encapsulates shoreline displacement forced by wave-driven cross-shore sediment transport. Hysteresis effects are shown to be important and are included in the model, whereby present shoreline change is influenced by past hydro-/morpho-dynamic conditions. The potential magnitude of shoreline change increases with incident wave power and the degree of disequilibrium. The latter disequilibrium term (Ω_eq − Ω) is expressed in terms of the time-evolving equilibrium (Ω_eq) and instantaneous (Ω) dimensionless fall velocities and dictates the direction of shoreline movement. Following Wright et al. (1985) the equilibrium fall velocity is defined as a function of the weighted antecedent conditions and is a proxy for the evolving beach state. The decay rate of the weighting function used to compute Ω_eq is a model free parameter determined by calibration against measured data, which physically reflects the degree of observed ‘memory’ of the system. The decay in amplitude of this weighting function with time is controlled by a ‘memory decay’ term (ϕ), where the weighting reaches 10%, 1% and 0.1% at ϕ, 2ϕ and 3ϕ days prior to the current calculation time. The model is applied to two multi-year (6 + years) data sets incorporating hourly wave and weekly shoreline measurements, from two contrasting energetic sites in SE Australia. The first is the relatively dissipative, straight Gold Coast (QLD) and the second is a more intermediate embayed beach at Narrabeen (NSW). The model shows significant skill at hindcasting shoreline change at both sites, predicting approximately 60% of the total shoreline variability. The Gold Coast shoreline is dominated by a strong seasonal signal. Conversely, at the Narrabeen embayment, shoreline variability (and morphology) is more dynamic, responding at storm frequency. Evidence suggests that there is a strong coherence between the shoreline position and morphodynamic state and that both have response times characterised by ϕ. It is hypothesised that optimised ϕ values in the shoreline model physically relate to the efficiency of sediment exchanges between the shoreface and offshore bars and the prevalence of one- or two-dimensional horizontal circulation. The general success of this new shoreline model for hindcasting the observed shoreline behaviour at two distinctly different open-coast sites suggests that this approach may be suitable for broader application.     

A global analysis of multi-mode sea surface temperature pattern

1 IntroductionThe variability of the air -sea system orches-trates a complex climate system of our earth, andthis variability gives rise to an array of naturally oc-curring dynamical modes at different time scales.These modes are important attributes of c…     

20世纪太平洋海温变化中人为因子与自然因子贡献的模拟研究

基于中国科学院大气物理研究所大气科学和地球流体力学国家重点实验室(LASG/IAP)发展的气候系统模式FGOALS_gl对20世纪太平洋海温变化的模拟,讨论了自然因子和人为因子对20世纪太平洋海温变化的相对贡献。观测资料表明,20世纪太平洋平均的SST变化主要分为3个时段:20世纪上半叶的增暖,40—70年代的微弱变冷,70年代之后的迅速增暖。20世纪太平洋SST变化的主导模态是全海盆尺度的振荡上升模态,其次为PDO振荡型,在70年代末PDO存在明显的年代际转型。通过全强迫试验、自然强迫试验、控制试验对上述现象进行归因分析,结果表明,人为因子和内部变率都对第一次增暖有贡献,而人类活动(主要是温室气体的增加)是70年代之后太平洋SST迅速增暖的主要原因。分区域来看,在两个增暖时段中,影响黑潮延伸体区SST变化的主要是自然因子和内部变率,影响其它海域SST变化的则主要是人为因子。全强迫试验可以较好的模拟出前两个模态的空间分布及时间序列。在没有人为因子的影响下,PDO成为太平洋海温变化的主导模态,其年代际转变发生在60年代中期,意味着人为因子是全海盆振荡增暖的主导原因,并且它使得年代际转型滞后了10a。因此,自然因子是导致SST年代际转型中的主导因子,人为因子有"调谐"作用。     

20世纪90年代后期南海上层海温变化趋势的转折

In this paper, the interdecadal variability of upper-ocean temperature in the South China Sea(SCS) is investigated based on several objectively analyzed data sets and two reanalysis data sets. The trends of the SCS sea surface temperature(SST) have changed from warming to cooling since the late 1990 s. A heat budget analysis suggests that the warming of the surface mixed layer during 1984–1999 is primarily attributed to the horizontal heat advection and the decrease of upward long wave radiation, with the net surface heat flux playing a damping role due to the increase of upward latent and sensible heat fluxes. On the other hand, the cooling of the surface mixed layer during 2000–2009 is broadly controlled by net surface heat flux, with the radiation flux playing the dominant role. A possible mechanism is explored that the variation of a sea level pressure(SLP) over the North Pacific Ocean may change the prevailing winds over the SCS, which contributes to the change of the SST in the SCS through the horizontal heat advection and heat fluxes.     

热带太平洋气候变率的三类模态及与ENSO强度变化的关系

基于Kaplan等重建的1856—2001年全球海表水温距平(SSTA)资料，用小波变换分析了热带太平洋SSTA的气候变率，对热带太平洋SSTA分别进行2—8、8—30和30—100a带通滤波，然后进行EOF分解。结果发现，ENSO模态具有5a左右的年际变化和15a左右的年代际变化2种显著周期，当二者位相相同时，ENSO事件加强，当二者位相相反时，ENSO事件减弱，当年际变化不明显时，显著的年代际变化也可单独导致ENSO事件；热带太平洋SSTA气候态变率以西太平洋暖池和赤道两侧的热带中东太平洋明显海温同号异常为主要特征，具60a左右的周期，其相位变化与气候跃变及El Nifio事件的类型有密切联系；长期增温倾向加大了El Nifio事件的振幅。文章最后指出，ENSO事件强度变化是由年际、年代际和气候态等3类模态变率共同作用的结果，在ENSO预报模式中考虑并引入年代际和气候态变化对ENSO循环的影响，是提高ENSO预测水平的有效途径之一。     

沙坝海岸沿岸流速度剖面特征研究

通过对两个坡度沙坝地形沿岸流实验测量和基于能量方程的沿岸流数值模拟,研究了沙坝海岸平均沿岸流速度剖面的双峰剖面特征,重点分析了第二个峰值的特征和两峰值的比值。综合考虑入射波高、入射波类型和坡度对波生沿岸流垂直岸线速度剖面的影响。结果表明,平均沿岸流速度剖面出现双峰剖面特征:第一峰值发生在沙坝向岸侧面的中部,第二个峰值发生在靠近岸线处;同一坡度情况两个峰值的位置和比值,不受入射波类型、入射波高的影响。数值模型中包括了侧混、底摩擦和水滚等因素,其数值模拟结果和实验值拟合较好,并讨论了有无侧混和水滚对速度剖面的影响。     

Can the gold coast beaches withstand extreme events?

The Gold Coast sandy beaches of Queensland (Australia) are exposed to energetic wave conditions. Storms, particularly tropical cyclones, have a high potential of destruction. The Gold Coast has not experienced excessive erosive events over the past 30 years. However, some climate indicators suggest that cyclone frequency is likely to increase in response to global climate change within the near future. Over a 2-month period in early 2006, beach surveys were undertaken with a theodolite total station at four different sites. Offshore wave conditions were provided by SWAN regional wave modelling. During this study, the Gold Coast was exposed to three major storms, the first one being the second most energetic over the past 30 years. Results show a substantial variability of the beach response to these events along the Gold Coast, and that engineering structures do not have marked effects. Easterly swells have the greatest impact on the Gold Coast sub-aerial beach morphology. When low wave-energy conditions prevail, the southern Gold Coast beaches recover more quickly than the northern ones, as they are sheltered from high SE waves and draw advantage from the artificial sand bypassing system. Nevertheless, the data show that the Gold Coast beaches are exceedingly fragile. For instance, the early March decadal event considerably weakened the beaches, which resulted in surprisingly high erosion rates all along the Gold Coast during the two following annual wave events. This study suggests that the Gold Coast beaches would not be able to withstand the impact of an increased frequency of extreme events similar in scale to those of 1967.     

Comparison of long-, medium- and short-term variations of beach profiles with and without submerged geological control

Victoria Beach (Cadiz, Spain) comprises a rocky flat outcrop in its northern zone and a sand-rich southern zone. These natural features allowed for a 5-year monitoring period and subsequent analysis of two different profiles (one in each zone) based on differences in bottom contours. Topo-bathymetric data were analysed using empirical orthogonal functions (EOFs) to determine changes over the short-, medium- and long-term. Several morphologic phenomena were identified (generalised erosion, seasonal or summer–winter tilting of the profile around different hinge points, berm development and its posterior destruction, etc.) in terms of their importance in explaining the variability of the collected data for both profiles. It is worth mentioning that both profiles undergo parallel regression in the medium-term. Thus, the 1st eigenfunction enabled us to identify the true regression of the beach shoreline, independent of seasonal or summer–winter slope changes. Reconstruction of profiles using EOF components demonstrated that though accretion periods in the medium-term were similar for both types of profiles, the accretion speed was much faster in the sand-rich profile than in the reef-protected profile (1.01 m³/day versus 0.33 m³/day). Moreover, the seasonal erosion rate and the subsequent shoreline retreat for the sand-rich profile were much larger than for the reef-protected profile (121 m³/year versus 29 m³/year). Analysis in the short-term (changes induced by a single day's storm) showed an instantaneous tilting of the profile, with the mobilised sand volume being much greater for the sand-rich than for the reef-protected profile (68 m³/m versus 12 m³/m).     

An investigation of the multi-scale temporal variability of beach profiles at Duck using wavelet packet transforms

In an earlier paper a particular discrete wavelet transform (DWT) was used to study the complex variation of beach profile changes. However, use of the DWT requires that the sequence of spatial and temporal resolution is fixed as a dyadic sequence, which means that the variability over longer intervals is not characterised well. Here we introduce the discrete wavelet packet transform (DWPT) that uses an adaptive scaling to partition the data variance, according to an entropy cost function. The advantages of this approach are demonstrated by its application to the study of temporal variability of a 22 year record of beach profile data from the Field Research Facility (FRF) at Duck, North Carolina, USA. Time series of beach elevations at three locations across a particular profile are investigated in detail. We conclude that the DWPT provides a superior analysis of non-stationary time series to that of the DWT, with improved resolution of the scale intervals of the variability. The beach elevation around the shoreline is shown to respond at both sub-annual and interannual scales, but variability at an annual scale is weak. Moving seaward into deeper water, the variance is partitioned into fewer and longer scales. It is confirmed that elevation changes around the inner bar at Duck exhibit a strong interannual variation consistent with Plant et al. (Plant, N.G., Holman, R.A. and Freilich, M.H., 1999. A simple model for interannual sandbar behaviour. Journal of Geophysical Research 104(C7), 15755–15776). Around 23% of the variance around the inner bar is explained at the temporal scale of 64–128 months, which is consistent with the bar behaviour of 6 years found by Ruessink et al. (Ruessink, B. G., Wijnberg, K. M., Holman, R. A., Kuriyama, Y. and Van Enckevort, I. M. J., 2003. Intersite comparison of interannual nearshore bar behaviour. Journal of Geophysical Research, 108 (C8): 1–12). A significant new finding is, however, that about 26% of the variance is attributable to temporal scales of 16–21.3 months. Reconstruction of the wavelet packet components for individual temporal scales is shown to provide a means for identifying the impact and scale of non-stationary events, such as storms, on the beach response. This provides further information that can be used to interpret the morphological changes in terms of the forcing processes and also serves to inform morphodynamic modelling.     

Beach nourishments at Coolangatta Bay over the period 1987–2005: Impacts and lessons

Erosion of the southern Gold Coast beaches (SE Queensland, Australia) was exacerbated after the extension of the Tweed River training walls in the early 1960s. To achieve the objective of restoring and maintaining beach amenity, significant nourishment works have been undertaken in Coolangatta Bay over the past 30 years. Particularly, under the Tweed River Entrance Sand Bypassing Project (TRESBP) since 1995, a number of nourishment campaigns and the implementation of a permanent sand bypass system in 2001 have resulted in significant changes of Coolangatta Bay morphology. The present case study investigates the influence of both wave climate and nourishment works on the area extending from the updrift Snapper Rocks area to downdrift Kirra Beach. SWAN spectral wave model is implemented at Coolangatta Bay area and forced by the global wave model WW3 to estimate wave forcing and the potential natural longshore drift entering in Coolangatta. Specific transects extracted from accurate bathymetric surveys are used to investigate and quantify Coolangatta Bay sedimentation for the period 1987–2005. A network of Argus video stations provides high sample rate information on the shoreline evolution. Results show that, over the past 10 years, Coolangatta Bay has infilled rapidly. Sedimentation reached up to 6 m in some areas between 1995 and 2005, with beach width increasing by 200 m at Kirra Beach. Rapid seaward shoreline migration is consistent with the intense over-pumping of sand relative to the natural potential to move sand alongshore. The nourishment strategy used during this project has successfully delivered large amounts of sand to the southern Gold Coast embayment, although it has been up to now controversial from many community perspectives. The artificial sand bypassing process proved to be much more efficient than depositing the dredged sand in the nearshore area which requires a significant period of low energy condition in order for the deposited sediment to migrate shoreward and weld to the shore. This case study confirms that, when carefully undertaken, sand bypassing is a sustainable and flexible soft engineering approach which can work in concert with natural processes.     

Analysis of sea surface height variabilities in the Kuroshio Current region by using Geosat altimeter data

INTRODUCTIONBeing a current of high temperature and high salinity, the Kuroshio carries a large amount ofheat from low latitude tropical ocean to high latitude ocean, and plays an imPOrtant role in theheat balance in East Asia. The variability of the Kurosl,io can affect the climate of East Asia, aswell as the ocean environment and the fishery resources. A lot of studies showed that the variabilitiies of the Kuroshio were related to the global changes especially to the onset of ENSO.…     

用TOPEX/POSEIDON高度计数据研究南极绕极流流域海面高度的低频变化

采用TOPEX/POSEIDON(T/P)卫星高度计 1 993年 1月— 2 0 0 0年 1 2月海面高度数据 ,研究包含了整个南极绕极流流系 (40°— 6 0°S)的海面高度低频变化。首先采用EOF分解方法获取南大洋时空分布的主要模态 ,前 3个EOF模态分别占总方差的 2 4 .8%、1 3 .8%和 1 0 .7%。然后采用EMD方法分别分析了各个EOF模态的时间系数曲线的组成成分 ,对南极绕极流海域的各种时间尺度变化给出了清晰的描述 ,对于不同尺度变化所占的比例得到了定量的结果。研究结果表明 ,EOF的各个模态不仅在形态上存在差异 ,而且具有相互独立的物理背景。EOF的第一模态主要体现了以太阳辐射冬夏差异形成的年周期变化 ,另一个显著的特征就是南极绕极流从 1 993— 2 0 0 0年海面的整体上升趋势。EOF的第二模态体现了陆地地形对南极绕极流的约束作用 ,同时也显示了ENSO过程对南极绕极流 ,特别是对南太平洋的海面高度变化的影响。EOF的第三模态则体现了南极绕极流对南大洋表面风场东西方向不均匀变化的响应。同时 ,本文的研究也证明了EOF与EMD方法联合使用对揭示大范围时空变化有重要的实际意义     

北太平洋海面异常风场的时空分布特征与海气热量交换

用北太平洋（含赤道太平洋区）１９４９～１９７９年的ＣＯＡＤＳ资料，通过矢量ＥＯＦ分解得到北太平洋异常风场的分布型及其时间变化规律。分析表明，ＥＯＦ１～５场与大气活动中心、海洋相互作用有联系，具有明显的天气学意义。此外，还讨论了ＥＯＦ异常风场间的转换及其季节性差异。     

A simple new shoreline change model

A simple new shoreline change model has been developed and calibrated/evaluated with several sets of high quality field data. The model is based upon the general observation that the shoreline tends to approach an equilibrium position exponentially with time when subjected to constant forcing. The model represents the shoreline response to cross-shore processes only and is extremely efficient, requiring only readily obtainable wave and water-level data as input. Shoreline changes are forced by changes in the local water surface elevation due to a combination of local tide, storm surge and wave-induced setup. The model contains three adjustable parameters, representing a baseline condition from which equilibrium shoreline displacements are calculated, and two rate constants, all of which are evaluated by minimizing the error between model hindcasts and several historical shoreline data sets. Several possible forms for the rate parameters, incorporating local wave and sediment properties, were considered and evaluated. At most sites, the model has proven successful in predicting large-scale shoreline response to local water level and wave forcing. The combination of model accuracy and efficiency, along with the minimal data required to drive the model, make it a potentially useful tool in many coastal engineering applications. As more high-quality shoreline, wave and water-level data sets become available, significant improvements can be made in the determination of the rate parameter governing the time scale of the beach response.