M2 model of the global ocean tide derived from SEASAT altimetry

Abstract

The recovery of ocean tides from satellite altimetry, an attractive alternative to the hydrodynamical‐numerical approach, is investigated to create a global model of the M2 tide. From the outline of the difficulties faced in altimetry interpretation, we bring out general guidelines to extract the tidal information from a short span of measurements. In particular, we discuss the choice of a reference surface and the effect of the orbit error and tidal aliasing on the recovery. From space‐time harmonic analyses of twenty‐four days of SEASAT altimetry, we derive M2 solutions expanded into series of surface spherical harmonics for the Indian, Pacific, and Atlantic Oceans separately and for the world ocean. The M2 cotidal maps we obtain feature qualitatively realistic tidal patterns and are consistent with the deep sea gages data. We then cast the bases to estimate the error budget of the altimeter tide solutions. The M2 fundamental harmonics involved in tidal energetics are evaluated from a spectral convolution of the global solutions with the ocean function and are used to test and discuss our results.

The present tidal recoveries must still be considered as preliminary trials because they are strongly dependent on the limits of the SEASAT mission and subject to improvements via an updating of our analysis procedure. But the altimeter approach of the open ocean tide modelling proves to be efficient, and the objective—to produce highly reliable models with the support of the next generation of satellite altimeters—is reasonably optimistic.     

Testing recent global ocean tide models with loading gravimetric data

As soon as altimetric data from Topex/Poseidon satellite were available, several ocean tide models were able to be constructed by different teams in response to the scientific community request. Here we present a complement to a first comparison study made with ten tidal models ( and , 1996). We use five more models of which some are updated versions computed using longer time series of altimetric data. The loading tide effects predicted by these models are compared to a data base of 228 gravimetric stations provided by the International Center for Earth Tides ( , 1994). Global statistical tests provide us with the relative performances of the models. Merging the five new models with the ten previous models allows us to make more general conclusions. CSR3.0 ( , 1994) remains the best of the fifteen models for the M₂ constituent (standard deviation of 0.425 μgal). For the O₁ constituent, Schwiderski ( , 1980) with a standard deviation of 0.298 μgal, gives the best results. When considering only regional subsets of gravimetric data, no ocean tide model systematically performs better than any other.     

基于z坐标海洋模式的全球正压潮波数值模拟研究

The performance of a z-level ocean model, the Modular Ocean Model Version 4(MOM4), is evaluated in terms of simulating the global tide with different horizontal resolutions commonly used by climate models. The performance using various sets of model topography is evaluated. The results show that the optimum filter radius can improve the simulated co-tidal phase and that better topography quality can lead to smaller rootmean square(RMS) error in simulated tides. Sensitivity experiments are conducted to test the impact of spatial resolutions. It is shown that the model results are sensitive to horizontal resolutions. The calculated absolute mean errors of the co-tidal phase show that simulations with horizontal resolutions of 0.5° and 0.25° have about 35.5% higher performance compared that with 1° model resolution. An internal tide drag parameterization is adopted to reduce large system errors in the tidal amplitude. The RMS error of the best tuned 0.25° model compared with the satellite-altimetry-constrained model TPXO7.2 is 8.5 cm for M_2. The tidal energy fluxes of M_2 and K_1 are calculated and their patterns are in good agreement with those from the TPXO7.2. The correlation coefficients of the tidal energy fluxes can be used as an important index to evaluate a model skill.     

A hybrid coordinate ocean model for shelf sea simulation

The general circulation in the North Sea and Skagerrak is simulated using the hybrid coordinate ocean model (HYCOM). Although HYCOM was originally developed for simulations of the open ocean, it has a design which should make it applicable also for coastal and shallow shelf seas. Thus, the objective of this study has been to examine the skills of the present version of HYCOM in a coastal shelf application, and to identify the areas where HYCOM needs to be further developed. To demonstrate the capability of the vertical coordinate in HYCOM, three experiments with different configurations of the vertical coordinate were carried out. In general, the results from these experiments compares quite well with in situ and satellite data, and the water masses and the general circulation in the North Sea and Skagerrak is reproduced in the simulations. Differences between the three experiments are small compared to other errors, which are related to a combined effect of model setup and properties of the vertical mixing scheme. Hence, it is difficult to quantify which vertical coordinate configuration works best for the coastal region. It is concluded that HYCOM can be used for simulations of coastal and shelf seas, and further suggestions for improving the model results are given. Since HYCOM also works well in open ocean and basin scale simulations, it may allow for a realistic modelling of the transition region between the open ocean and coastal shelf seas.     

基于海洋潮汐动力模型的水位改正方法研究

本文研究并提出了一种基于海洋潮汐动力模型的水位改正方法。该方法通过对数值模拟的天文潮位进行改正,结合残差改正获得特定站的潮位数据。结合实际资料,将基于海洋潮汐动力模型的水位改正方法与传统的水位改正方法(时差法和最小二乘潮位拟合法)进行了比较,新方法改正的精度明显高于传统方法,显示其在地形变化较为复杂海域进行水位改正的可行性与独特优势。该方法可以在海洋测绘中减少短期验潮站的布设,用于潮位序列缺失的修补。     

A harmonic approach to global ocean tide analysis based on TOPEX/Poseidon satellite

The constant and harmonic parts of the global ocean tide are modeled by up to nine major tidal constituents, namely, S2, M2, N2, K1, P1, O1, Mf, Mm, and Ssa. Our computations start with the Fourier sine and cosine series expansion for the tidal constituents, including the constant Mean Sea Level (MSL). Although the frequencies of the tidal constituents are considered known, the coefficients of the sine and cosine functions are assumed to be unknown. Subsequently, the coefficients of the sine and cosine functions, as well as the constant part of the Fourier expansion, were expanded into spherical harmonics up to degree and order n, where n corresponds to the number of linearly independent spherical harmonic base functions needed to model the tidal constituents, determined via independent columns of the Gram matrix. The unknown coefficients of the spherical harmonic expansions are computed using sea level observations within cycles #1–#350 of the TOPEX/Poseidon satellite altimetry over 11 years of its mission. A set of orthonormal base functions was generated for the marine areas covered by TOPEX/Poseidon observations from the spherical harmonics using a Gram-Schmidt orthogonalization process. These were used for modeling the dominant tidal constituents. The computed models based on orthonormal base functions for the nine tidal constituents and the constant part of the Fourier expansion, were tested numerically for their validity and accuracy, proving centimeter accuracy.     

一个高分辨率太平洋-印度洋海盆环流模式的初步结果

利用LASG/IAP发展的一个0.25°×0.25°高分辨率太平洋-印度洋海盆环流模式,初步分析了模式在太平洋区域的模拟结果,并与海洋同化资料以及前人的研究结果作比较,检验此模式对该区域平均气候态、年际变化的模拟能力。分析表明,模式较好地再现了海表温度（SST）分布、赤道温跃层和纬向流结构、赤道流系分布形态、海表高度以及正压流函数空间分布特征;同时,对显著的El Ni?o和La Ni?a事件的模拟等方面与Simple Ocean Data Assimilation（SODA）2.0.2版本结果相近。此外,模式模拟北赤道流（NEC）分叉点位置的季节和年际变化以及吕宋海峡流量的年际变化与已有研究结果基本一致。进一步分析还发现,在年际尺度上,NEC分叉点位置和吕宋海峡流量与ENSO密切相关。     

Preliminary results of the global ocean tide derived from HY-2A radar altimeter data

The HY-2A satellite, which is equipped with a radar altimeter and was launched on August 16, 2011, is the first Chinese marine dynamic environmental monitoring satellite. Extracting ocean tides is one of the important applications of the radar altimeter data. The radar altimeter data of the HY-2A satellite from November 1, 2011 to August 16, 2014 are used herein to extract global ocean tides. The constants representing the tidal constituents are extracted by HY-2A RA data with harmonic analysis ...     

Sub-seasonal variability of Luzon Strait Transport in a high resolution global model

The Luzon Strait is the main impact pathway of the Kuroshio on the circulation in South China Sea (SCS). Based on the analysis of the 1997–2007 altimeter data and 2005–2006 output data from a high resolution global HYCOM model, the total Luzon Strait Transport (LST) has remarkable subseasonal oscillations with a typical period of 90 to 120 days, and an average value of 1.9 Sv into SCS. Further spectrum analysis shows that the temporal variability of the LST at different depth is remarkable different. In the upper layer (0–300 m), westward inflow has significant seasonal and subseasonal variability. In the bottom layer (below 1 200 m), eastward outflow exhibits remarkable seasonal variability, while subseasonal variability is also clear. In the intermediate layer, the westward inflow is slightly bigger than the eastward outflow, and both of them have obvious seasonal and subseasonal variability. Because the seasonal variation of westward inflow and eastward outflow is opposite, the total transport of intermediate layer exhibits significant 50–150 days variation, without obvious seasonal signals. The westward Rossby waves with a period of 90 to 120 days in the Western Pacific have very clear correlationship with the Luzon Strait Transport, this indicates that the interaction between these westward Rossby waves and Kuroshio might be the possible mechanism of the subseasonal variation of the LST.     

Accuracy assessment of global ocean tide models in the South China Sea using satellite altimeter and tide gauge data

In this study, to meet the need for accurate tidal prediction, the accuracy of global ocean tide models was assessed in the South China Sea(0°–26°N, 99°–121°E). Seven tide models, namely, DTU10, EOT11 a, FES2014, GOT4.8,HAMTIDE12, OSU12 and TPXO8, were considered. The accuracy of eight major tidal constituents(i.e., Q₁, O₁, P₁,K₁, N₂, M₂, S₂ and K₂) were assessed for the shallow water and coastal areas based ...     

全球大洋潮汐模式在北印度洋潮汐预报准确性的评估

为评估DTU10、TPXO8、GOT00.2和NAO.99b 4个全球大洋潮汐模式对北印度洋潮汐的预报能力,采用英国海洋资料中心提供的海区中部和沿岸站潮汐调和常数资料,检验了这些模式4个主要分潮(M_2、S_2、K_1、O_1)的准确度。它们的各分潮调和常数资料准确度都比较高,振幅绝均差的最大值仅5.61 cm,迟角绝均差的最大值仅9.13°。这些模式的调和常数给出潮波传播特征差别不大。基于这些模式提供的调和常数,分别建立了北印度洋4、8和16分潮潮汐预报模型,将预报结果与中国海事服务网提供的沿岸24个站潮汐表资料进行对比。各模式的8分潮(M_2、S_2、N_2、K_2、K_1、O_1、P_1、Q_1)潮汐预报模型均优于4分潮(M_2、S_2、K_1、O_1)潮汐预报模型,NAO.99b模式可以提供16分潮(M_2、S_2、N_2、K_2、K_1、O_1、P_1、Q_1、MU_2、NU_2、T_2、L_2、2N_2、J_1、M1、OO_1)潮汐预报模型,但是对预报结果改善不明显;在各模式中,GOT00.2模式的8分潮潮汐预报模型对北印度洋沿岸的预报效果最好,平均绝均差为14.97 cm。     

High resolution downscaled ocean waves (DOW) reanalysis in coastal areas

Large-scale wave reanalysis databases (0.1°–1° spatial resolution) provide valuable information for wave climate research and ocean applications which require long-term time series (> 20 years) of hourly sea state parameters. However, coastal studies need a more detailed spatial resolution (50–500 m) including wave transformation processes in shallow waters. This specific problem, called downscaling, is usually solved applying a dynamical approach by means of numerical wave propagation models requiring a high computational time effort. Besides, the use of atmospheric reanalysis and wave generation and propagation numerical models introduce some uncertainties and errors that must be dealt with. In this work, we present a global framework to downscale wave reanalysis to coastal areas, taking into account the correction of open sea significant wave height (directional calibration) and drastically reducing the CPU time effort (about 1000 ×) by using a hybrid methodology which combines numerical models (dynamical downscaling) and mathematical tools (statistical downscaling). The spatial wave variability along the boundaries of the propagation domain and the simultaneous wind fields are taking into account in the numerical propagations to performance similarly to the dynamical downscaling approach. The principal component analysis is applied to the model forcings to reduce the data dimension simplifying the selection of a subset of numerical simulations and the definition of the wave transfer function which incorporates the dependency of the wave spatial variability and the non-uniform wind forcings. The methodology has been tested in a case study on the northern coast of Spain and validated using shallow water buoys, confirming a good reproduction of the hourly time series structure and the different statistical parameters.     

A reduced grid for a parallel global ocean general circulation model

A limitation of many global climate models with explicit finite-difference numerics is the timestep restriction caused by the decrease in cell size associated with the convergence of meridians near the poles. To keep the longitudinal width of model cells as uniform as possible, we apply a “reduced” grid to a three-dimensional primitive equation ocean-climate model. With this grid the number of cells in the longitudinal direction is reduced at high latitudes. The grid consists of subgrids which interact at interfaces along their northern and southern boundaries, where the resolution changes by a factor of three. We extend the finite-difference techniques to these interfaces, focusing on the conservation required to perform long time integrations, while preserving the staggered spatial arrangement of variables and the numerics used on subgrids. The common alternative used to reduce the timestep restriction caused by the spherical grid is the filtering of high-frequency modes from the high-latitude solution. The reduced grid allows an increased timestep while eliminating the need for filtering and reduces execution time per model step by roughly 20%. We implement the reduced grid model for parallel computer architectures with two-dimensional domain decomposition and message passing, with speedup results similar to those of the original model. We present results of model runs showing small effects on the solution and sizable improvements to the execution time.     

Evaluation of ocean model ventilation with CFC-11: comparison of 13 global ocean models

We compared the 13 models participating in the Ocean Carbon Model Intercomparison Project (OCMIP) with regards to their skill in matching observed distributions of CFC-11. This analysis characterizes the abilities of these models to ventilate the ocean on timescales relevant for anthropogenic CO₂ uptake. We found a large range in the modeled global inventory (±30%), mainly due to differences in ventilation from the high latitudes. In the Southern Ocean, models differ particularly in the longitudinal distribution of the CFC uptake in the intermediate water, whereas the latitudinal distribution is mainly controlled by the subgrid-scale parameterization. Models with isopycnal diffusion and eddy-induced velocity parameterization produce more realistic intermediate water ventilation. Deep and bottom water ventilation also varies substantially between the models. Models coupled to a sea-ice model systematically provide more realistic AABW formation source region; however these same models also largely overestimate AABW ventilation if no specific parameterization of brine rejection during sea-ice formation is included. In the North Pacific Ocean, all models exhibit a systematic large underestimation of the CFC uptake in the thermocline of the subtropical gyre, while no systematic difference toward the observations is found in the subpolar gyre. In the North Atlantic Ocean, the CFC uptake is globally underestimated in subsurface. In the deep ocean, all but the adjoint model, failed to produce the two recently ventilated branches observed in the North Atlantic Deep Water (NADW). Furthermore, simulated transport in the Deep Western Boundary Current (DWBC) is too sluggish in all but the isopycnal model, where it is too rapid.     

宫古海峡通道海流的高分辨率数值模拟

运用美国麻省理工大学MITgcm模式、模式嵌套技术和高分辨率网格(水平方向为1°/48×1°/48,垂向为22层),模拟了宫古海峡通道中的海流流动状况。流场不同分辨率的模拟结果表明,海底地形对宫古海峡通道中的海流流动影响显著;宫古海峡通道中的海流流动结构具有如下特征:垂向流动可分为3层,每层均存在流速核心;400 m以浅的上层海流从太平洋流入到东海,平均流速约为10 cm/s,流速核心位于160 m附近;400~1 000 m的中层海流从东海流出到太平洋,平均流速约为2 cm/s,流速核心位于650 m附近;1 000 m以下的深层海流从太平洋流入到东海,平均流速约为1 cm/s,流速核心位于1 200 m附近。宫古海峡通道中的海流流动具有较强的季节变化特征,秋末冬初流动较强,夏季流动较弱。     

ARGO data assimilation into the ocean dynamics model with high spatial resolution using Ensemble Optimal Interpolation (EnOI)

The article proposes parallel implementation of the Ensemble Optimal Interpolation (EnOI) data assimilation (DA) method in eddy-resolving World Ocean circulation model. The results of DA experiments in North Atlantic with ARGO drifters are compared with the multivariate optimal interpolation (MVOI) DA scheme. The sensitivity of the model error, i.e., the difference between the model and observations depending on the number of ensemble elements, is also assessed and presented. The effectiveness of this method over the MVOI scheme is confirmed. The model outputs with and without assimilation are also compared with independent sea surface temperature data from ARMOR 3d.     

The Max-Planck-Institute global ocean/sea ice model with orthogonal curvilinear coordinates

The Hamburg Ocean Primitive Equation model has undergone significant development in recent years. Most notable is the treatment of horizontal discretisation which has undergone transition from a staggered E-grid to an orthogonal curvilinear C-grid. The treatment of subgridscale mixing has been improved by the inclusion of a new formulation of bottom boundary layer (BBL) slope convection, an isopycnal diffusion scheme, and a Gent and McWilliams style eddy-induced mixing parameterisation. The model setup described here has a north pole over Greenland and a south pole on the coast of the Weddell Sea. This gives relatively high resolution in the sinking regions associated with the thermohaline circulation. Results are presented from a 450 year climatologically forced integration. The forcing is a product of the German Ocean Model Intercomparison Project and is derived from the European Centre for Medium Range Weather Forecasting reanalysis. The main emphasis is on the model’s representation of key quantities that are easily associated with the ocean’s role in the global climate system. The global and Atlantic northward poleward heat transports have peaks of 1.43 and 0.84 PW, at 18° and 21° N respectively. The Atlantic meridional overturning streamfunction has a peak of 15.7 Sv in the North Atlantic and an outflow of 11.9 Sv at 30° S. Comparison with a simulation excluding BBL shows that the scheme is responsible for up to a 25% increase in North Atlantic heat transport, with significant improvement of the depths of convection in the Greenland, Labrador and Irminger Seas. Despite the improvements, comparison with observations shows the heat transport still to be too weak. Other outstanding problems include an incorrect Gulf Stream pathway, a too strong Antarctic Circumpolar Current, and a too weak renewal of Antarctic Intermediate Water. Nevertheless, the model has been coupled to the atmospheric GCM ECHAM5 and run successfully for over 250 years without any surface flux corrections.     

Estimation of baroclinic tide energy available for deep ocean mixing based on three-dimensional global numerical simulations

The global distributions of the major semidiurnal (M₂ and S₂) and diurnal (K₁ and O₁) baroclinic tide energy are investigated using a hydrostatic sigma-coordinate numerical model. A series of numerical simulations using various horizontal grid spacings of 1/15–1/5° shows that generation of energetic baroclinic tides is restricted over representative prominent topographic features. For example, nearly half of the diurnal (K₁ and O₁) baroclinic tide energy is excited along the western boundary of the North Pacific from the Aleutian Islands down to the Indonesian Archipelago. It is also found that the rate of energy conversion from the barotropic to baroclinic tides is very sensitive to the horizontal grid spacing as well as the resolution of the model bottom topography; the conversion rate integrated over the global ocean increases exponentially as the model grid spacing is reduced. Extrapolating the calculated results in the limit of zero grid spacing yields the estimate of the global conversion rate to be 1105 GW (821, 145, 102, 53 GW for M₂, S₂, K₁, and O₁ tidal constituents, respectively). The amount of baroclinic tide energy dissipated in the open ocean below a depth of 1000 m, in particular, is estimated to be 500–600 GW, which is comparable to the mixing energy estimated by Webb and Suginohara (Nature 409:37, 2001) as needed to sustain the global overturning circulation.