Bayesian perspective of the unconventional approach for assimilating aliased radar radial velocities

The global minimization problem for directly assimilating aliased radial velocities is derived in terms of Bayesian estimation by folding the domain of the original Gaussian non-aliased observation probability density function (pdf) into the Nyquist interval. By truncating the folded tails of the observation pdf, the observation term in the costfunction recovers the aliased observation term formulated previously by an unconventional approach. This establishes the theoretical basis for the unconventional approach and quantifies the involved approximation. The alias-robust radar wind analysis developed based on the unconventional approach is also revisited from the Bayesian perspective.     

Doppler radar radial winds in HIRLAM. Part I: observation modelling and validation

An observation operator for Doppler radar radial wind measurements is developed further in this article, based on the earlier work and considerations of the measurement characteristic. The elementary observation operator treats radar observations as point measurements at pre-processed observation heights. Here, modelling of the radar pulse volume broadening in vertical and the radar pulse path bending due to refraction is included to improve the realism of the observation modelling.
The operator is implemented into the High Resolution Limited Area Model (HIRLAM) limited area numerical weather prediction (NWP) system. A data set of circa 133 000 radial wind measurements is passively monitored against the HIRLAM six-hourly background values in a 1-month experiment. No data assimilation experiments are performed at this stage. A new finding is that the improved modelling reduces the mean observation minus background (OmB) vector wind difference at ranges below 55 km, and the standard deviation of the radial wind OmB difference at ranges over 25 km.
In conclusion, a more accurate and still computationally feasible observation operator is developed. The companion paper (Part II) considers optimal super-observation processing of Doppler radar radial winds for HIRLAM, with general applicability in NWP.     

TOPEX/POSEIDON高度计浅海潮汐混淆的初步分析

根据对卫星轨道特征和观测结果的分析,对TOPEX/POSEIDON(简称T/P)星载高度计在我国近海的潮致混淆现象进行了初步研究.分析表明,在浅海区T/P高度计的观测结果存在很强的潮致高频混淆.NASA分发的地球物理记录中所提供的潮汐订正值虽适用于大洋,但不能有效地除去浅海潮汐.虽然如此,T/P潮致混淆的主要频段的周期小于90d,因而可以通过滤波方法提取周期较长的海面高度季节信号,从而用于季节环流(如南海季风环流)的研究.采用FFT/IFFT方法滤波试验的结果显示,T/P的海面高度观测结果有很高的精度,滤波处理后的海面高度距平变化和地面潮位观测结果一致性良好,上、下行轨道交叉处相邻测点间的标准偏差在3cm左右,可满足南海环流研究的需要.     

Doppler radar radial winds in HIRLAM. Part II: optimizing the super-observation processing

Doppler radar radial wind observations are modelled in numerical weather prediction (NWP) within observation errors which consist of instrumental, modelling and representativeness errors. The systematic and random modelling errors can be reduced through a careful design of the observation operator (Part I). The impact of the random instrumental and representativeness errors can be decreased by optimizing the processing of the so-called super-observations (spatial averages of raw measurements; Part II).
The super-observation processing is experimentally optimized in this article by determining the optimal resolution for the super-observations for different NWP model resolutions. A 1-month experiment with the HIRLAM data assimilation and forecasting system is used for radial wind data monitoring and for generating observation minus background (OmB) differences. The OmB statistics indicate that the super-observation processing reduces the standard deviation of the radial wind speed OmB difference, while the mean vector wind OmB difference tends to increase. The optimal parameter settings correspond at a measurement range of 50 km (100 km) to an averaging area of 1.7 km² (7.3 km²).
In conclusion, an accurate and computationally feasible observation operator for the Doppler radar radial wind observations is developed (Part I) and a super-observation processing system is optimized (Part II).     

引入差比关系法分析西北太平洋TOPEX/POSEIDON卫星高度计测高数据

TOPEX/POSEIDON(T/P)卫星高度计数据信息中存在周期成分混淆问题.对其中的一类混淆引入差比关系方法对混淆的分潮进行分离.卫星轨道交叉点资料包括升轨和降轨资料,资料量比沿轨点资料多1倍,经分析发现:在已有为期6a多的观测资料时间序列中,在沿轨处混淆的分潮如K₁和SSA在交叉点处不再混淆,可以直接分离.因此首先对交叉点资料进行调和分析.然后由交叉点的分析结果得到分潮间的差比关系,处理到相近的沿轨点处,从而得到沿轨点的调和常数.用引入差比关系方法,对西北太平洋海区6a多的T/P卫星高度计资料进行了潮汐分析,并与沿岸及岛屿验潮站资料进行了比较,所得结果较满意.     

Tidal Effects on Determining a Point at the Bottom of the Sea by Combining GPS and Sonar Observations

This paper discusses tidal effects on an observation scheme to determine a point at the bottom of the sea by combining GPS and Sonar observations. For the purpose, three kinds of Earth tides are introduced (i.e., the crust tide, the equipotential surface point (ocean depth) tide, and the geoid tide). The corresponding mathematical expressions are derived to demonstrate the tidal effects on GPS and Sonar observations. The relations between the Earth tides are also discussed. Theoretical results imply a very interesting conclusion, namely that, for a local area, the static position of a point at the bottom of sea can be obtained by the dynamic observations without any tidal correction. Actually, the tidal effects cancel each other in the mentioned observation scheme. It therefore indicates that the observation scheme is free of tidal effects. Furthermore, we learned that the divergence caused by any error source on ocean surface is canceled and does not affect the final results. Therefore, to determine the position of a point at the bottom of sea, we need not consider any tidal effects.     

舟山海域高频地波雷达表层流探测试验

2015年4月7-30日,在浙江省舟山近海海域开展了“嵊山-朱家尖”小型阵列变频高频地波雷达系统的海上比测试验,通过雷达观测数据与定点ADCP海流资料的比对检验了地波雷达表层流探测性能。径向流比对结果显示,测点与雷达法向夹角越小,距离雷达距离越近,径向流比测结果越好,雷达探测的结果越可靠。嵊山站径向流与ADCP观测结果的各站总体平均误差为7.98 cm/s,平均均方根误差为15.34 cm/s,平均相关系数为0.89,朱家尖站径向流与ADCP观测结果的各站总体平均误差为6.24 cm/s,平均均方根误差为12.36 cm/s,平均相关系数为0.81。根据矢量流比对结果显示,矢量流速与ADCP观测结果的各站总体平均误差为4.82 cm/s,平均均方根误差为15.03 cm/s,平均相关系数为0.44。设置在嵊山、朱家尖两个雷达站双站探测的核心区域（两个雷达站连线的中垂线上,并且与两个雷达站构成一个近似直角三角形）的站点比测结果更加理想,当流速大于0.25 m/s时,对于核心区域平均后的流向均方根误差为24.9°。     

Tidal Effects on Determining a Point at the Bottom of the Sea by Combining GPS and Sonar Observations

This paper discusses tidal effects on an observation scheme to determine a point at the bottom of the sea by combining GPS and Sonar observations. For the purpose, three kinds of Earth tides are introduced (i.e., the crust tide, the equipotential surface point (ocean depth) tide, and the geoid tide). The corresponding mathematical expressions are derived to demonstrate the tidal effects on GPS and Sonar observations. The relations between the Earth tides are also discussed. Theoretical results imply a very interesting conclusion, namely that, for a local area, the static position of a point at the bottom of sea can be obtained by the dynamic observations without any tidal correction. Actually, the tidal effects cancel each other in the mentioned observation scheme. It therefore indicates that the observation scheme is free of tidal effects. Furthermore, we learned that the divergence caused by any error source on ocean surface is canceled and does not affect the final results. Therefore, to determine the position of a point at the bottom of sea, we need not consider any tidal effects.     

Tidal harmonic analysis of TOPEX/POSEIDON data in the Northwest Pacific by introducing difference-ratio relations

The difference-ratio relations are introduced to separate tidal constituents that are aliaseddue to the sampling interval and sampling span of the TOPEX/POSEIDON altimeter. It is found that some tidal constituents such as K_1 and SSA, though aliased at along track points, are not aliased at crossover points Ixrausf the data at crossover points are double those at along track points. So the harmonic analysis method can be employed directly for the analysis of time series at crossover points. Then the difference-ratio relations from crossover points are introduced to analyze the time series at along track points. The TOPEX/POSEIDON data in the Northwest Pacific are analyzed with this method. The results from this method agree well with tidal constants from tidal gauges.     

A densely sampled core and climate variable aliasing

Undersampled records are susceptible to aliasing, in which a high frequency appears incorrectly as a lower one. We study the sampling requirements in a core taken from Rockall Trough using bulk density, P-wave velocity, and magnetic susceptibility as measured on an automated system. At 2-cm spacing (approximately 33 years in this core), all variables show a characteristic red-noise behavior, but with a spectral slope that is sufficiently weak so that significant aliasing appears to be present. P-wave velocity shows the largest potential corruption, probably owing to the weaker spatial averaging present in the sensor. Approximately 50% of the apparent low-frequency energy is aliased in all variables at some frequencies in both quiet and active regions of the record. In this core, a sampling interval of 0.2 cm appears to be "safe" in both active and quiet portions of the core, aliasing little or no energy, except in the P-wave record. For cores of different duration, sampling interval, and measurement type, the considerations will be identical, the importance of the problem depending directly upon the shape of the overall spectrum describing the entire frequency (wavenumber) range of physical variability.     

象山港牛鼻山水道潮流场的高频地波雷达观测与分析

作为LORCE计划中构建高频地波雷达观测网的试点,面向象山港牛鼻山水道,在六横岛郭巨山和白马礁各设置了1台OSM AR-S50高频地波雷达.在2台雷达合成表面流场有效区域的中间地带,利用Valeport旋桨式海流仪和ADCP定点开展了周日连续观测,以验证高频地波雷达合成表面流场的精度.对比定点流场和高频地波雷达对应数据...     

A New Methodology for Incorporating Tide Gauge Data in Sea Surface Topography Models

As part of the Vertical Offshore Reference Frames (VORF) project sponsored by the U. K. Hydrographic Office, a new model for Sea Surface Topography (SST) around the British Isles has been developed. For offshore areas (greater than 30 km from the coast), this model is largely derived from satellite altimetry. However, its accuracy and level of detail have been enhanced in coastal areas by the inclusion of not only the 60 PSMSL tide gauges with long-term records around the coasts of the United Kingdom and Ireland but also some 385 gauges established at different epochs and for different observation spans by the U. K. Admiralty. All tide gauge data were brought into a common reference frame by a combination of datum models and direct GPS observations, but a more significant challenge was to bring all short-term sea level observations to an unbiased value at a common epoch. This was achieved through developing a spatial-temporal correlation model for the variations in mean sea level around the British Isles, which in turn meant that gauges with long-term observation spans could be used as control points to improve the accuracy of Admiralty gauges. It is demonstrated that the latter can contribute point observations of mean sea level (MSL) with a precision of 0.078 m. A combination of least squares collocation and interpolation was developed to merge the coastal point and offshore gridded data sets, with particular algorithms having to be developed for different configurations of coastal topology. The resulting model of sea surface topography is shown to present a smooth transition from inshore coastal areas to offshore zones. Further benefits of the techniques developed include an enhanced methodology for detecting datum discontinuities at permanent tide gauges.     

Spurious instabilities of long planetary waves in a two-and-a-half layer model subtropical gyre ocean with a wind-driven steady circulation

In a number of flows that support coupled free-waves, instability results when free-wave dispersion relations calculated without the coupling cross or approach one another. The propagation of long planetary wave perturbations of a two-and-a-half layer model subtropical gyre is one such oceanographically important instance. This note points out that, for a baroclinically unstable two-and-a-half layer model subtropical gyre, numerically aliased long wave dispersion relation plots display extra crossings that are artifacts of the discretization, and these may lead both to spurious numerical instabilities and to numerical misrepresentation of actual instabilities. Paradoxically, the numerical instability may in some instances manifest itself more strongly as the numerical resolution is improved. The aliasing mechanism may be related to the zone of small scale activity found in the southwestern corner of a time dependent model subtropical gyre in the numerical perturbation experiments of (Dewar, W., Huang, R., 2001. Adjustment of the ventilated thermocline. J. Phys. Oceanogr. 13, 293–309). Similar multilayer models are often discussed in the literature, so that the results may be widely useful.     

基于VMD对SAR海洋内波参数的自动反演

经验模态分解(empirical mode decomposition,简称EMD)是反演海洋内波参数的有效方法之一,但由于EMD存在模态混叠等问题,对海洋内波进行参数反演时会产生一定误差。相比较于EMD,变分模态分解(variational mode decomposition,简称VMD)能够有效地抑制模态混叠现象。为了更好地对海洋内波进行参数反演,提出了一种基于VMD对合成孔径雷达(synthetic aperture radar,简称SAR)遥感图像中的内波参数进行自动反演的方法。该方法先对SAR图像进行Canny处理,获取图像中的内波条纹信息,再根据内波传播方向自动选取灰度剖面;然后利用集合经验模态分解(ensemble empirical mode decomposition,简称EEMD)信号特征自适应分解模态函数的特点,再将分解得到的有效模态数作为VMD中参数K的参考值;最后利用VMD分解后的数据进行内波参数反演。试验结果表明:通过对Canny预处理后的条纹信息进行灰度剖面自动选取,解决了人为选取剖面所可能导致的误差;通过对剖面信号进行VMD处理不仅解决了EMD模态混叠的问题,成功地反演出内波的前导波振幅,而且所反演的结果与EEMD反演参数以及实测资料数据吻合得很好。     

Global point‐mass adjustment of the oceanic geoid based on satellite altimetry

Altimeter residuals from a global spherical‐harmonic adjustment of satellite altimetry can be used as observations in a subsequent, or second‐phase, adjustment of a short‐wavelength oceanic geoid in terms of point‐mass magnitudes as parameters. An important part of the development presented is the formulation of the second‐phase adjustment via a banded or a banded‐bordered system of normal equations. This task encompasses three separate features: (1) elimination of the point masses from an observation equation if they are sufficiently far from the pertinent observation point, (2) special arrangement of the point‐mass parameters in the adjustment scheme, and (3) resolution of the resulting system through an adaptation of the well‐known Choleski algorithm. If only the point‐mass magnitudes are subject to adjustment, one is concerned with a banded system of normal equations. If selected tidal parameters are also implicated, this system becomes banded‐bordered. In fact, the former is a special case of the latter in every respect. By virtue of this approach (with or without tidal parameters), geoid undulations over large ocean basins can be adjusted in a few overlapping strips of point masses, leading to a detailed resolution of the entire oceanic geoid.     

导波式雷达水位计在潮位观测中的应用

文中简要介绍了雷达水位计的测量原理、分类和技术特点,并将其中的导波式雷达水位计和非接触式雷达水位计与传统的浮子式水位计进行了比较,说明了导波式雷达水位计应用于一些特定条件下潮位观测的优势。基于导波式雷达水位计设计了一套水位观测系统。简要介绍了该水位观测系统的系统组成、硬件设计、软件设计。针对该水位观测系统进行了计量检定,并进行了现场安装试验。在现场实验中将导波式雷达水位计数据与浮子式水位计数据进行比较,说明了采用该设计方案进行潮位观测的可行性。     

用GPS水准法测定单点垂线偏差

介绍了利用GPS和水准高差观测数据计算单点垂线偏差的理论与方法,系统地分析了测定垂线偏差的误差源,研究了观测方案与成果质量的关系,提出了保证垂线偏差测定精度的观测设计准则。通过与天文大地方法观测结果的实例比较,验证了该方法的有效性。     

The statistical observation localized equivalent-weights particle filter in a simple nonlinear model

This paper presents an improved approach based on the equivalent-weights particle filter(EWPF) that uses the proposal density to effectively improve the traditional particle filter. The proposed approach uses historical data to calculate statistical observations instead of the future observations used in the EWPF’s proposal density and draws on the localization scheme used in the localized PF(LPF) to construct the localized EWPF. The new approach is called the statistical observation localized E...