Fully normalized spherical cap harmonics: application to the analysis of sea-level data from TOPEX/POSEIDON and ERS-1

We introduce two sets of fully normalized harmonics for the spectral analysis of functions defined on a spherical cap. The harmonics are the products of Fourier functions and the fully normalized associated Legendre functions of non-integer degree. Using Sturm-Liouville theory for boundary-value problems, we present two convenient and stable formulae for computing the zeros of the associated Legendre functions that form two sets of orthogonal functions. Formulae for the stable numerical evaluation of the fully normalized associated Legendre functions of non-integer degree that avoid the gamma function are also derived. The result from the expansions of sea-level anomaly from altimetry into Set 2 fully normalized cap harmonics shows fast convergence of the series, and the degree variances decay rapidly without aliasing effects. The zero-degree coefficients (Set 2) of sea-level anomaly from TOPEX/ POSEIDON (T/P) and ERS-1 indicate an El Niño event during 1993 January-1993 July, and a La Niño event during 1993 November-1994 July, although the ERS-1 result is less obvious. Ocean circulations over the South China Sea and the Kuroshio area are clearly identified with the low-degree expansions of sea-surface topography (SST) from T/P and ERS-1. A cold-core eddy of 4° in diameter centred at 17.5°N, 118 E was detected with the expansion of SST from T/P cycle 47, and a property of the cap harmonics is used to compute this eddy's kinetic energy. The kinetic energy is at a low in winter and high in summer, and its variation seems to be periodic with an amplitude of 0.4 m² S^-2.     

Low-frequency sea-level fluctuations along the coasts of Namibia and South Africa

Summary. Sea-level records at nine ports along the coasts of Namibia and South Africa are used to establish the existence of coastal trapped disturbances in sea-level as a response to the passage of synoptic weather systems. Using spectral analysis the characteristics and spatial variability of the sea-level fluctuations are identified. The results of cross-correlation analyses performed on sea-level data at adjacent ports for two periods during 1982 are discussed in detail to examine the propagation of coastal trapped waves round the coast.     

The grade index model as a rationale for autogenic nonequilibrium responses of deltaic clinoform to relative sea-level rise

Grade index (G_index) is a dimensionless number given as the volume-in-unit-time ratio of subaerial allocation to both subaerial and subaqueous allocations of sediment supplied to a delta from upstream. It was originally proposed for understanding the effect of basin water depth on the morphodynamics of delta distributary channels under stationary relative sea level. We here examine how rising relative sea level modulates the G_index, using geometrical reasoning and numerical simulations. We find that the grade index model can account for autoretreat of the deltaic shoreline, autodrowning of the whole system, and autobreak of the deltaic sedimentation, all of which are the consequences of autogenic nonequilibrium responses to steadily rising relative sea level. The regressive-to-transgressive threshold (i.e. the onset of autoretreat) is crossed when the delta plain's dimensionless basal area (A_t*) encounters a critical value that is expressed in terms of G_index: regression and transgression are sustained when A_t* is below and above the threshold, respectively. The mode of transgression depends on the slope conditions. If the hinterland slope (γ) is steeper than the foreset slope (β), both A_t* and G_index decrease as the relative sea-level rises. Eventually, the depositional system experiences autodrowning when A_t* = G_index = 0. If γ < β; on the other hand, both A_t* and G_index increase. This latter slope condition eventually causes autobreak of the deltaic sedimentation, afterward of which A_t* = G_index = 1. The grade index model is useful for interpreting and predicting the stratigraphic responses of natural deltaic clinoforms in conditions of rising relative sea level.     

Quantifying sand delivery to deep water during changing sea-level: Numerical models from the Quaternary Brazos Icehouse continental margin

Sequence stratigraphy for clastic continental margins predicts the development of sand-rich turbidite deposits during specific times in relation to base-level cycles. It is now widely understood that deltas can extend to the shelf-edge forced by high sediment flux and/or base level, providing a direct connection to transfer sediment and sand to the slope and basin floor even during high base level periods. Herein, we build a stratigraphic forward model for the last 120 kyr of the fluvio-deltaic to deep-water Brazos system (USA) where sediment partitioning along an Icehouse continental margin can be evaluated. The reduced-complexity stratigraphic forward model employs geologically constrained input parameters and mass balance. The modelled architecture is consistent with the location of depositional units previously mapped in the shelf. Sand bypasses the shelf and upper slope between 35 to 15 kyr before present and only about 20%–30% of all the sediment and sand supplied to the system is transferred to deep water. Several scenarios based on the initial Brazos model investigate the relationships between base level and deep-water sand ratio (DWSR). DWSR is defined as the relative amount of sand transferred to the deep-water portions of the system subdivided by the total sand input to the model. Linear correlations between DWSR and base level change rates or base level are very poor. Short-term variability due to local processes (for example avulsions) is superimposed to the long-term trends and mask the base level signal. DWSR for an entire base-level cycle is mainly controlled by the proportion of time the delta stays docked at the shelf-edge. Stratigraphic forward models are useful to complement field observations and quantify how different processes control stratigraphy, which is important for making predictions in areas with limited information.     

Oceanic excitation of daily to seasonal signals in Earth rotation: results from a constant-density numerical model

Velocity and mass fields from a constant-density, near-global ocean model, driven with observed twice-daily surface wind stresses and atmospheric pressures for the period October 1992-September 1993, are used to calculate oceanic excitation functions for the length of day (LOD) and for polar motion (PM), and results are analysed as a function of the frequency band. Variable currents and mass redistributions are both important in determining oceanic excitation functions. For bands with periods longer than one month, wind-driven variability is the primary cause of oceanic excitation signals. At higher frequency bands, larger deviations from the inverted barometer response occur, and pressure-driven signals contribute more significantly to the variance in the excitation functions. Oceanic LOD excitation is generally small compared to that of the atmosphere, except for the 2-10 day band. At these scales, adding oceanic to atmospheric excitation series does not lead to better agreement with the observed LOD, although this result may be related to data quality issues. With regard to the excitation of PM, the ocean is in general as important as the atmosphere at most time scales. Combined oceanic and atmospheric excitation series compare visibly better with geodetic series than do atmospheric series alone, pointing to the ocean as a source of measurable signals in PM.     

基于SSA和MGF的海面变化长期预测及对比

海面变化预测受到建模思路、方法选择、数据长度及数据质量等因素的影响,导致了海面变化预测的不确定性。本文以国内6个验潮站自20世纪50年代以来的月平均潮位序列为基础,采用奇异谱分析(SSA)与均值生成函数(MGF)模型相结合的方案,以各站位最初20余年数据为基础建立预测模型,以后续年份的实测数据进行了多方案对比验证及检验。预测试验显示MGF模型具有较高的预测精度,并表现出较好的长期预测的稳定性特点。以SSA去噪序列为基础,应用MGF模型预测了各站位至2050年的月尺度海面值,年均值计算结果表明至2050年海面波动上升的幅度不超过20cm,海面变化速率同样表现出阶段性和波动性。与前人相关研究成果对比表明,本文所采用的SSA与MGF相结合的预测结果具有可比性,在方法原理和验证结果上看具有较好的长期预测潜力。     

Relative sea-level control on the building of two distinct shelf-margin clinothems on the late-Quaternary Pearl River margin: Insights from numerical stratigraphic forward modelling

As one of the most important forcing factors, relative sea-level changes exert a major influence on the building of shelf-margin clinothems. However, it is still not well understood how these changes control the growth of shelf edges and the condition of sediments transporting into deep water, especially over the individual-clinothem scale of several 100 ky. On the late-Quaternary Pearl River margin, there are two distinct shelf-margin clinothems: SQ3 and SQ4. They have different shelf-edge trajectories (slight rising vs. steep rising) and different styles of deep-water deposition (fan lobes consisting mainly of MTDs vs. fan lobes consisting mainly of turbidites). This work takes those SQ3 and SQ4 as study objects and runs a total of 136 experiments from the Dionisos stratigraphic forward model to investigate how relative sea-level changes control the trajectories of shelf edges and the volumes of MTDs in deep water over the individual-clinothem scale. Our quantitative results suggest that under the geological background of high sediment supply on the late-Quaternary Pearl River margin, the duration of highstand systems tracts (HST) relative to lowstand systems tracts (LST) or forced regressive systems tracts (FST) has a significant influence on the building of individual shelf-margin clinothems. If the relative duration of HST is either very short or very long, slight-rising shelf-edge trajectories and large-volume MTDs would be formed, whereas if the relative duration of HST is comparable with LST or FST, steep-rising shelf-edge trajectories and limited MTDs would be formed. Through the constrains of the model set to the real geological condition of the SQ3 and SQ4 clinothems, it is found that SQ3 was caused by the quite long relative duration of HST, which made highstand deltaic systems advance over the pre-existing shelf-slope break, leading to significant accretion and instability of the shelf edge and thus, giving rise to the formation of slight-rising shelf-edge trajectories and fan lobes with high MTDs contents. SQ4, however, formed as a result of the comparable durations of HST, LST, and FST, which made highstand deltaic systems advance to but not beyond the previous shelf-slope break allowing the subsequent FST to be directly perched on the clinoform slope. Such building processes did not drive pronounced accretion and instability of the shelf edge and thus, caused the formation of steep-rising shelf-edge trajectories and fan lobes with low MTDs contents.