On dynamically consistent eddy fluxes

The role of mesoscale oceanic eddies in driving the large-scale currents is studied in an eddy-resolving, double-gyre ocean model. The new diagnostic method is proposed, which is based on dynamical decomposition of the flow into the large-scale and eddy components. The method yields the time history of the eddy forcing, which can be used as additional, external forcing in the corresponding non-eddy-resolving model of the gyres. The main strength of this approach is in its dynamical consistency: the non-eddy-resolving solution driven by the eddy forcing history correctly approximates the original large-scale flow component. It is shown that statistical decompositions, which are based on space-time filtering diagnostics, are dynamically inconsistent. The diagnostics algorithm is formulated and tested, and the diagnosed eddies are analysed, both statistically and dynamically. It is argued that the main dynamic role of the eddies is to maintain the eastward-jet extension of the subtropical western boundary current (WBC). This is done largely by both the time–mean isopycnal-thickness flux and the relative-vorticity eddy flux fluctuations. The fluctuations drive large-scale flow through the nonlinear rectification mechanism. The relative-vorticity flux contributes mostly to the eastward jet meandering. Finally, eddy fluxes driven by both the eddies and the large-scale flow are found to be important. The latter is typically neglected in the analysis, but here it corresponds to important large-scale feedback on the eddies.     

Local instability in a periodically forced sliced cylinder

This paper investigates the dynamics of mesoscale eddy generation by instability of time-varying flows. Laboratory experiments on oscillatory motion over topography in a rapidly rotating cylinder have shown that isolated mesoscale eddies, which form in the sidewall boundary layer during certain phases of the forcing cycle, are associated with the onset of chaotic behavior in this system. This paper explores the origin of these eddies by performing computational simulations of the flow, and then interpreting the results of the calculations using spatially localized and quasi-static linear stability theory. For most of the experimental parameter space the quasi-geostrophic simulations are in excellent agreement with the laboratory observations. The eddies arise as a barotropic shear flow instability in regions of space and at times where the inflection points of the instantaneous large-scale flow are farthest from the sidewall, and where Fjortoft's theorem is strongly satisfied. At finite amplitude, advection of the local wavetrains up the bottom slope strengthens the anticyclonic eddies. These then merge, leading in most circumstances to a single strong anticyclonic vortex that can leave the sidewall and penetrate the interior. When parameters are such that the eddy persists all the way around the basin and back to the local instability region, the flow is observed to become chaotic.     

Spatial and temporal variability of major ocean currents and mesoscale eddies

A global picture of ocean current variability may be obtained by analyzing surface drift currents in terms of their mean and eddy kinetic energies. High values for both quantities are found in the western boundary currents and in the equatorial current system; low values are found in the interior of major gyres. However, nowhere are eddy energies less than 200 cm² s^–2, indicating that, even in the least energetic parts of the oceans, surface speeds of ~20 cm s^–1 prevail. Recent experimental studies also support the widespread occurrence of mesoscale mid-oceanic eddies. Another type of eddy is abundant in the vicinity of boundary currents: examples include Gulf Stream Rings, the Great Whirl of the Somali Current, and disturbances of the predominantly zonal equatorial flow manifested by large-scale meandering about the equator. Recent numerical models using low-viscosity and high-resolution computational grids also reveal the ubiquitous existence of mesoscale structures. The importance of eddies is that they seem to be energetic enough and sufficiently widespread so as to play some part — not yet understood — in the circulation of the world ocean. Speculative analogies to the atmosphere suggest that the mesoscale ocean eddies are the storms and weather systems of the sea. We need global statistics on their distribution, their occurrence in various oceanic regions, their dimensions, and their lifetimes. The prospect of even a single global oceanic weather map, comparable to those obtained daily for the atmosphere, is hopeless in terms ofin situ oceanographic observations. Remote sensing may provide a partial solution.In the past, sea-surface temperature observations by satellites have revealed cold and warm eddies shed by western boundary currents. Satellite observations, moreover, have shown the thermal effects of continental shelf waves and areas with pronounced upwelling. These phenomena are characterized by strong temperature gradients and relatively large differences in surface elevation. Mid-ocean eddies are far more subtle and difficult to observe since they possess smaller differences of temperature and sea-surface topography. Three representative examples, including recent experimental results in western boundary currents, the equatorial region, and a typical mid-ocean region, are discussed in detail. Typical signals of temperature and sea-level topography, as well as typical temporal and spatial scales of the observed phenomena, are given.     

The exchange of fluid mass between quasi-geostrophic and ageostrophic motions during the reflection of Rossby waves from a coast. I. The case of an infinite rectilinear coast

When the problem of the reflection of spatially localized Rossby waves from a coast is treated using the quasigeostrophic (QG) approximation, the total fluid mass and the along-shore circulation calculated from the geostrophic height field are not conserved. To understand the correct mass balance and the degree to which the QG equations and boundary conditions may be in error, we analyze an initial-value problem for the Laplace tidal equations on a β-plane in the asymptotic limit 1, where is the ratio of the spatial scale of the motion to the Earth's radius.It is shown that there is a coupling between QG and O() fields. Physically, the coupling occurs by a peculiar adjustment process in the O() approximation in which fast gravity waves are permanently generated to build up a quasi-stationary edge Kelvin wave. Different temporal scales (large for O(1) Rossby waves and small for the O() gravity waves make comparable the contributions of the waves to the mass and circulation balance equations. However, QG analysis itself describes the reflection of Rossby waves correctly, but is incomplete, and for satisfactory balances one has to take into account the fields of both orders of the approximation.Applications of the results to closed basins, baroclinicity, and variable bottom topography are discussed. It is conjectured that an interaction of strong oceanic eddies with a coast (continental slope) may give rise to noticeable along-shore jet currents.     

Atmospheric Response to Mesoscale Ocean Eddies over the South China Sea

The South China Sea(SCS) is an eddy-active area. Composite analyses based on 438 mesoscale ocean eddies during 2000–2012 revealed the status of the atmospheric boundary layer is influenced remarkably by such eddies. The results showed cold-core cyclonic(warm-core anticyclonic) eddies tend to cool(warm) the overlying atmosphere and cause surface winds to decelerate(accelerate). More than 5% of the total variance of turbulent heat fluxes, surface wind speed and evaporation rate are induced by mesoscale eddies. Furthermore, mesoscale eddies locally affect the columnar water vapor, cloud liquid water, and rain rate. Dynamical analyses indicated that both variations of atmospheric boundary layer stability and sea level pressure are responsible for atmospheric anomalies over mesoscale eddies. To reveal further details about the mechanisms of atmospheric responses to mesoscale eddies, atmospheric manifestations over a pair of cold and warm eddies in the southwestern SCS were simulated. Eddy-induced heat flux anomalies lead to changes in atmospheric stability. Thus, anomalous turbulence kinetic energy and friction velocity arise over the eddy dipole, which reduce(enhance) the vertical momentum transport over the cold(warm) eddy, resulting in the decrease(increase) of sea surface wind. Diagnoses of the model's momentum balance suggested that wind speed anomalies directly over the eddy dipole are dominated by vertical mixing terms within the atmospheric boundary layer, while wind anomalies on the edges of eddies are produced by atmospheric pressure gradient forces and atmospheric horizontal advection terms.     

大气对黑潮延伸区中尺度海洋涡旋的响应——冬季暖、冷涡个例分析

采用动态合成、带通滤波等方法,通过对冬季黑潮延伸区暖、冷两个中尺度海洋涡旋的分析,研究了大气对中尺度海洋涡旋的响应特征。结果表明,海表温度（SST）与近海面风速的正相关关系在涡旋的动态合成图上清晰可见,暖（冷）涡上空对应10 m风速的极大（小）值,即海洋对大气的强迫作用在日时间尺度上表现显著;SST高低值中心基本对应10 m风无辐散区,暖（冷）涡上空为异常正（负）涡度分布;暖（冷）涡上空潜热、感热通量增大（减小）,降低（增大）大气稳定度,从而加强（减弱）边界层垂直混合作用,使得海洋大气边界层增厚（变薄）。暖（冷）涡旋上空对应摩擦速度极大（小）值,反映了湍流粘性力在高（低）海温中心增大（减小）的特征,表明动量垂直混合机制在中小尺度海气相互作用中起着主要作用。中尺度海洋涡旋能够影响大气瞬变扰动,大气瞬变扰动强度在暖（冷）涡下游上空出现极大（小）值,该影响不仅表现在海洋大气边界层,在自由大气中低层也有较为清晰的反映。此外,从能量转换的角度入手,发现斜压能量转换在中尺度海洋涡旋影响大气瞬变扰动强度中贡献明显。     

Heat balance and eddies in the Peru-Chile current system

The Peru-Chile current System (PCS) is a region of persistent biases in global climate models. It has strong coastal upwelling, alongshore boundary currents, and mesoscale eddies. These oceanic phenomena provide essential heat transport to maintain a cool oceanic surface underneath the prevalent atmospheric stratus cloud deck, through a combination of mean circulation and eddy flux. We demonstrate these behaviors in a regional, quasi-equilibrium oceanic model that adequately resolves the mesoscale eddies with climatological forcing. The key result is that the atmospheric heating is large (>50 W m^?2) over a substantial strip >500 km wide off the coast of Peru, and the balancing lateral oceanic flux is much larger than provided by the offshore Ekman flux alone. The atmospheric heating is weaker and the coastally influenced strip is narrower off Chile, but again the Ekman flux is not sufficient for heat balance. The eddy contribution to the oceanic flux is substantial. Analysis of eddy properties shows strong surface temperature fronts and associated large vorticity, especially off Peru. Cyclonic eddies moderately dominate the surface layer, and anticyclonic eddies, originating from the nearshore poleward Peru-Chile Undercurrent (PCUC), dominate the subsurface, especially off Chile. The sensitivity of the PCS heat balance to equatorial intra-seasonal oscillations is found to be small. We demonstrate that forcing the regional model with a representative, coarse-resolution global reanalysis wind product has dramatic and deleterious consequences for the oceanic circulation and climate heat balance, the eddy heat flux in particular.     

Loop Current Eddy formation and baroclinic instability

The formation of three Loop Current Eddies, Ekman, Franklin, and Hadal, during the period April 2009 through November 2011 was observed by an array of moored current meters and bottom mounted pressure equipped inverted echo sounders. The array design, areal extent nominally 89° W to 85° W, 25° N to 27° N with 30–50 km mesoscale resolution, permits quantitative mapping of the regional circulation at all depths. During Loop Current Eddy detachment and formation events, a marked increase in deep eddy kinetic energy occurs coincident with the growth of a large-scale meander along the northern and eastern parts of the Loop Current. Deep eddies develop in a pattern where the deep fields were offset and leading upper meanders consistent with developing baroclinic instability. The interaction between the upper and deep fields is quantified by evaluating the mean eddy potential energy budget. Largest down-gradient heat fluxes are found along the eastern side of the Loop Current. Where strong, the horizontal down-gradient eddy heat flux (baroclinic conversion rate) nearly balances the vertical down-gradient eddy heat flux indicating that eddies extract available potential energy from the mean field and convert eddy potential energy to eddy kinetic energy.     

Downstream development of baroclinic waves in the midlatitude jet induced by extratropical transition: A case study

This study uses eddy kinetic energy analysis and a targeting method to investigate how an extratropical transition(ET)event induced downstream development(the modification of the midlatitude flow downstream of the ET system) in the midlatitude jet environment. The downstream development showed distinct characteristics of "coupling development" and being "boundary-trapped". Eddies(potential disturbances) first developed at the upper levels, and these triggered lower-level eddy development, with all eddies decaying away from the tropopause and the surface. Thereafter, a lower-level eddy caught up with the upper-level eddy ahead of it, and they coupled to form a cyclone extending through the whole troposphere. Vertical ageostrophic geopotential flux may be a crucial dynamic factor throughout the eddy's lower-level growth, boundary-trapping,and coupling development.Together with barotropic conversion, the ageostrophic geopotential fluxes that were transported from Hurricane Fabian(2003) to the midlatitudes by the outflow led to downstream ridge development in the upper-level jet. The strong downstream advection of eddy kinetic energy in the exit region of the jet streak triggered downstream trough development. The well-known ridge–trough couplet thus formed. The vertical ageostrophic fluxes that were transported downward from the developed upper-level systems converged near the surface and resulted in lower-level eddy growth. Baroclinic conversion was negligible near the boundaries, while it was the main source of eddy kinetic energy at mid-levels. In the upper-level jet, potential energy was converted to the mean kinetic energy of the jet, which in turn was converted to eddy kinetic energy through barotropic conversion.     

Isolating mesoscale coupled ocean–atmosphere interactions in the Kuroshio Extension region

The Kuroshio Extension region is characterized by energetic oceanic mesoscale and frontal variability that alters the air–sea fluxes that can influence large-scale climate variability in the North Pacific. We investigate this mesoscale air-sea coupling using a regional eddy-resolving coupled ocean–atmosphere (OA) model that downscales the observed large-scale climate variability from 2001 to 2007. The model simulates many aspects of the observed seasonal cycle of OA coupling strength for both momentum and turbulent heat fluxes. We introduce a new modeling approach to study the scale-dependence of two well-known mechanisms for the surface wind response to mesoscale sea surface temperatures (SSTs), namely, the ‘vertical mixing mechanism’ (VMM) and the ‘pressure adjustment mechanism’ (PAM). We compare the fully coupled model to the same model with an online, 2-D spatial smoother applied to remove the mesoscale SST field felt by the atmosphere. Both VMM and PAM are found to be active during the strong wintertime peak seen in the coupling strength in both the model and observations. For VMM, large-scale SST gradients surprisingly generate coupling between downwind SST gradient and wind stress divergence that is often stronger than the coupling on the mesoscale, indicating their joint importance in OA interaction in this region. In contrast, VMM coupling between crosswind SST gradient and wind stress curl occurs only on the mesoscale, and not over large-scale SST gradients, indicating the essential role of the ocean mesocale. For PAM, the model results indicate that coupling between the Laplacian of sea level pressure and surface wind convergence occurs for both mesoscale and large-scale processes, but inclusion of the mesoscale roughly doubles the coupling strength. Coupling between latent heat flux and SST is found to be significant throughout the entire seasonal cycle in both fully coupled mode and large-scale coupled mode, with peak coupling during winter months. The atmospheric response to the oceanic mesoscale SST is also studied by comparing the fully coupled run to an uncoupled atmospheric model forced with smoothed SST prescribed from the coupled run. Precipitation anomalies are found to be forced by surface wind convergence patterns that are driven by mesoscale SST gradients, indicating the importance of the ocean forcing the atmosphere at this scale.     

Interpreting Reynolds stress from perspective of eddy geometry

Geometric features in oceanic mesoscale eddies such as tilt and anisotropy can influence the properties of the Reynolds stress that provides feedback between the eddies and the background flow. By regarding an eddy as a wave, previous studies have parameterized the Reynolds stress based on the equivalence in the tilt angle between the phase of the eddy stream functions and the variance ellipse for the Reynolds stress (RS-ellipse). However, the wave assumption cannot predict the anisotropy of the RS-ellipse, and also largely simplifies the eddy geometry, which would naturally be an ellipsoid rather than a wave. The present study explores the shape relation between elliptical eddies and the RS-ellipse, by mathematically reformulating the Reynolds stress based on the eddy shape. The new formula reveals that the shape relation is regulated by the horizontal extent of the occurrence probability distribution (PDF) of the eddy, and that the shape of the eddy and RS-ellipse are identical at the place of maximum PDF when the horizontal scale of the PDF is sufficiently larger than the size of the eddy. A similar tendency is found in eddies detected by satellite altimetry in the Kuroshio Extension jet region. A detailed analysis of the PDF in this region shows that the tilts of the eddies are likely to be consistent with the destabilization effect on the jet, suggesting a strong relation between the eddy geometry and the jet's stability in this region. These findings may open a path toward a new method to parameterize the Reynolds stress with the background state, exploiting the shape equivalence between the eddies and the RS-ellipse.     

A general rule for synoptic-eddy feedback onto low-frequency flow

In this study, scale interaction between synoptic eddies and low-frequency flow is investigated. It is demonstrated here that there is a general rule, the “left-hand rule”, that describes synoptic eddy feedback onto low-frequency flow. The rule is that low-frequency anomalies systematically stir and deform the transient eddies in such a way that the irrotational eddy-vorticity fluxes are directed preferentially about 90° toward the left-hand side of the low-frequency flow; thus this eddy feedback plays a positive role in maintaining and prolonging low-frequency flow under the stormy atmosphere. Similarly, we show that the irrotational eddy-temperature and moisture fluxes are also directed preferentially about 90° toward the left-hand side of the low-frequency flow in the northern hemisphere. The eddy-temperature fluxes and their vertical structure play a positive role in reinforcing the low-frequency flow in the low levels. The moisture fluxes play a role in enhancing low-frequency flow by providing eddy-induced moisture convergence and divergence.     

Characteristics and vertical structure of oceanic mesoscale eddies in the Bay of Bengal

The signatures of mesoscale eddies induced surface and subsurface changes have not been comprehensively quantified for the Bay of Bengal (BoB) region. This study quantifies the statistical properties and three-dimensional (3D) eddy structures in the BoB. To accomplish this, the satellite altimetry data combined with automated eddy detection and tracking algorithm is used. Horizontal distribution of surface characteristics of eddies is analyzed by using 24 years (1993–2016) of AVHRR infrared satellite sea surface temperature (SST) and 7 years (2010–2016) of sea surface salinity (SSS) of SMOS satellite data. Surface eddy centric composite analysis reveals the existence of warm (cold) and diverse SSS anomalies for anticyclonic (cyclonic) eddies. During winter, it is important to note that the eddy induced SST and SSS anomalies show the dipole patterns show opposite phases for the cyclonic and anticyclonic eddies. Observed diploe structures are consistent with the eddy rotation and background large-scale meridional gradient of temperature and salinity fields. The 3D structure of eddies is investigated by using the ARMOR3D and Argo float profiles. The horizontal distribution of temperature and salinity anomalies from ARMOR3D signify the monopole structure of eddies in the subsurface layers. Further, the analysis of composite averages of 241 (200) Argo temperature profiles indicates the core of anticyclonic (cyclonic) eddies centered at about ∼140 m (∼100 m). However, salinity profiles depict the existence of core at ∼65 m (∼50 m). This study have practical relevance to a variety of stakeholders and finds profound importance in the validation of eddy-resolving ocean models for the BoB region.     

黑潮延伸体海洋中尺度涡旋:四套数据的比较

在不同的中尺度涡数据中,涡旋的识别,跟踪方法以及物理参数的定义存在差异,因此需要对涡旋结果进行相互比较和验证.本文比较了Chelton,GEM-M,Faghmous和Dong四套中尺度涡数据在黑潮延伸体区域的基本特征.结果表明,各数据的中尺度涡数量,特征和轨迹均存在差异.经过归一化处理后,涡特征的地理分布和时间变化高度相似,特别是Chelton,Fahgmous和Dong三套数据.     

Interdecadal changes in mesoscale eddy variance in the Gulf of Alaska circulation: Possible implications for the Steller sea lion decline

Abstract

A distinct change in the ocean circulation of the Gulf of Alaska after the 1976–77 climate shift is studied in an eddy‐permitting primitive equation model forced by observed wind stresses from 1951–99. When the Aleutian Low strengthens after 1976–77, strong changes occur in the mean velocity of the Alaskan Stream and in its associated mesoscale eddy field. In contrast, the Alaska Current and the eddy flows in the eastern Gulf remain relatively unchanged after the shift. Since mesoscale eddies provide a possible mechanism for transporting nutrient‐ rich open‐ocean waters to the productive shelf region, the flow of energy through the food web may have been altered by this physical oceanographic change. This climate‐driven mechanism, which has a characteristic eastwest spatial asymmetry, may potentially help to explain changes in forage fish quality in diet diversity of Steller sea lions whose populations have declined precipitously since the mid‐1970s in the western Gulf while remaining stable in the eastern Gulf.     

Impacts of Increased SST Resolution on the North Pacific Storm Track in ERA-Interim

This study examines the artificial influence of increasing the SST resolution on the storm track over the North Pacific in ERA-Interim. Along with the mesoscale oceanic eddies and fronts resolved during the high-resolution-SST period, the low-level storm track strengthens northward, reaching more than 30% of the maximum values in the low-resolution-SST period after removing the influence of ENSO. The mesoscale structure firstly imprints on the marine atmospheric boundary layer, which then leads to changes in turbulent heat flux and near-surface convergence, forcing a secondary circulation into the free atmosphere, strengthening the vertical eddy heat, momentum and specific humidity fluxes, and contributing to the enhancement of the storm track. Results from a high-resolution atmospheric model further indicate the changes in the storm track due to the mesoscale SST and their relationship.     

基于潜标资料的中南半岛外海水文特征分析

基于2012年9月—2013年12月中南半岛外海累计16个月的长时间序列潜标观测数据,结合AVISO海表面高度异常（sea level anomaly,SLA）数据,首次详细分析了中南半岛外海典型中尺度涡的运动规律和垂向特征及其对环境水文特征的影响,揭示了该海域深层海流的时间变化特征。在观测期间共捕捉到3次中尺度涡过程,中尺度涡对站位所在海域主温跃层深度变化的最大影响振幅可达50 m。研究发现：1)观测站位所在海域各深度的温度异常时间变化与站位SLA时间变化的相关性随深度增加逐渐减弱。2)上层和中层的海水流动受中尺度涡影响显著。1 500 m和2 000 m的深层环流主要表现为季节变化;在强中尺度涡暖涡经过期间,中尺度涡能影响到1 500 m的环流场,同时出现30 d周期震荡。2 000 m流场则不受中尺度涡影响。3)中南半岛以东南海1 500 m处深层海流月平均流速夏季大于冬季,月平均可达3～5 cm·s-1;2 000 m处深层海流最大流速出现在冬季,月平均可达2～6 cm·s-1。深层海流受潮汐影响显著,潮汐作用主要影响深层海流东西向流速的变化。     

Coastal currents and eddies and their interaction with topography

The nonlinear interaction of vorticity driven coastal currents and eddies with topography is studied. The topography is either a semi-infinite escarpment perpendicular to the coast (such that topographic waves propagate toward the coast) or a semi-circular canyon or seamount attached to the coast. Assuming a piecewise constant potential vorticity distribution, the quasigeostrophic equations are solved using contour dynamics. Offshore propagating dipole eddies occur, whenever a coastal current or eddy interacts with escarpment and canyon topographies. The size and frequency at which dipoles form are found to depend on the vorticity of the current and amplitude of the topography. However, for a seamount, little eddy shedding is observed and the coastal current or eddy skirts around topography.     

涡动非地转位势通量对风暴轴维持的影响

通过对涡动动能方程和涡动有效位能方程的诊断分析，结果发现，斜压性是导致风暴轴入口区天气尺度涡动发展的最主要原因，而涡动发展后则主要通过非地转位势通量向下游频散能量而衰减，并进一步成为激发下游新的涡动活动发展的主要能量来源。因此，涡动非地转位势通量所引起的"下游发展效应"对风暴轴在东端弱斜压区的维持具有十分重要的作用。     

Oceanic mesoscale eddy in the Kuroshio extension: Comparison of four datasets: 黑潮延伸体海洋中尺度涡旋: 四套数据的比较

Some relatively mature mesoscale eddy products have been released for scientific purposes in recent decades. However, the metrics used to identify eddies, the tracking methods, and the definition of the physical parameters are all different across the different datasets, so intercomparisons and validation of these datasets are badly needed. Here, the authors intercompare the basic features of ocean mesoscale eddies in the Kuroshio extension region from four eddy datasets—namely, Chelton, GEM-M, Faghmous, and Dong. In the case study, eddy numbers and locations as well as the eddy tracks identified by the four datasets are compared for a specific date. The authors find that all the datasets have different eddy numbers, but more than 50% of identified eddies coincide. GEM-M, with the so-called “segmentation” algorithm, can identify considerably more eddies than others, while Chelton identifies fewer eddies due to tracking errors, which also lead to a long lifespan. From the analysis of the probability distribution function of eddy features, GEM-M eddies tend to have a larger amplitude and radius and Chelton tends to have long-life eddies. It is further found that the geographic distributions and temporal variation of normalized eddy features are highly similar among the four datasets—particularly among Chelton, Fahgmous, and Dong. In addition, the mean trajectories of the four datasets are generally overlapped initially, and then spread after 245 days. The findings help toward better understanding the uncertainties of eddy features in the Kuroshio extension region.摘要在不同的中尺度涡数据中, 涡旋的识别,跟踪方法以及物理参数的定义存在差异, 因此需要对涡旋结果进行相互比较和验证.本文比较了Chelton,GEM-M,Faghmous和Dong四套中尺度涡数据在黑潮延伸体区域的基本特征.结果表明, 各数据的中尺度涡数量,特征和轨迹均存在差异.经过归一化处理后, 涡特征的地理分布和时间变化高度相似, 特别是Chelton,Fahgmous和Dong三套数据.