Optimal estimation of Eddy viscosity and friction coefficients for a Quasi‐three‐dimensional numerical tidal model

Abstract

It is shown that the parameters in a quasi‐three‐dimensional numerical tidal model can be estimated accurately by assimilation of data from current meters and tide gauges. The tidal model considered is a semi‐linearized one in which advective nonlinearities are neglected but nonlinear bottom friction is included. The parameters estimated are the eddy viscosity, bottom friction coefficient, water depth and wind drag coefficient, the first three of which are allowed to be position‐dependent. The adjoint method is used to construct the gradient of a cost function defined as a certain norm of the difference between computed and observed current and surface elevations. On the basis of a number of tests, it is shown that very effective estimation of the nodal values of the parameters can be achieved using the current data either alone or in combination with elevation data. When random errors are introduced into the data, the estimated parameters are quite sensitive to the magnitude of the errors, and in particular the eddy viscosity is unstably sensitive. The sensitivity of the viscosity can be stabilized by incorporating an appropriate penalty term in the cost function or alternatively by reducing the number of estimated viscosity values via a finite element approximation. Once stabilized, the sensitivity of the estimates to data errors is significantly reduced by assimilating a longer data record.     

Air-sea Interaction of Typhoon Sinlaku （2002） Simulated by the Canadian MC2 Model

Three experiments for the simulation of typhoon Sinlaku (2002) over the western North Pacific are performed in this study by using the Canadian Mesoscale Compressible Community (MC2) atmospheric model. The objective of these simulations is to investigate the air-sea interaction during extreme weather conditions, and to determine the sensitivity of the typhoon evolution to the sea surface temperature (SST)cooling induced by the typhoon. It is shown from the three experiments that the surface heat fluxes have a substantial influence on the slow-moving cyclone over its lifetime. When the SST in the East China coastal ocean becomes 1℃ cooler in the simulation, less latent heat and sensible heat fluxes from the underlying ocean to the cyclone tend to reduce the typhoon intensity. The cyclone is weakened by 7 hPa at the time of its peak intensity. The SST cooling also has impacts on the vertical structure of the typhoon by weakening the warm core and drying the eye wall. With a finer horizontal resolution of (1/6)°×(1/6)°, the model produces higher surface wind, and therefore more surface heat fluxes are emitted from the ocean surface to the cyclone, in the finer-resolution MC2 grid compared with the relatively lower resolution of 0.25°×0.25°MC2 grid.     

Secular Trends in Tidal Parameters along the Coast of Japan

The secular trends for local tidal datums, tide ranges, and tidal harmonic constituents at 13 tidal gauge stations located along the coast of Japan were analyzed in this study. The general trends for mean higher high water (MHHW), mean high water (MHW), diurnal tide range (DTR), mean tide range (MTR), and relative mean sea level (RMSL) were positive, and for mean lower low water (MLLW) and mean low water (MLW) the trends were negative. The variation patterns were largest at Kushiro and Ofunato stations, both located in the open waters of the North Pacific Ocean. The tidal datums and tide ranges remained fairly stable at the Hakodate station, and an opposite trend was observed at the Maisaka station. The analysis of tidal harmonic constituents revealed a less pronounced pattern. The most distinct trend was observed for the M₂ amplitude, which appears to be negative at a majority of the stations. The largest decrease in the M₂ amplitude was observed at Kushimoto and Mera stations, also located in the open waters of the North Pacific Ocean. The negative trend is attributed to decreasing water depths at these stations, owing to small-scale local processes.     

On Measurements of the Tide at Churchill,Hudson Bay

Since the late 1990s the semi-diurnal tide at Churchill, on the western shore of Hudson Bay, has been decreasing in amplitude, with M₂ amplitudes falling from approximately 154?cm in 1998 to 146?cm in 2012 and 142?cm in 2014. There has been a corresponding small increase in phase lag. Mean low water, decreasing throughout most of the twentieth century, has levelled off. Although the tidal changes could reflect merely a malfunctioning tide gauge, the fact that there are no other measurements in the region and the possibility that the tide is revealing important environmental changes calls for serious investigation. Satellite altimeter measurements of the tide in Hudson Bay are complicated by the seasonal ice cover; at most locations less than 40% of satellite passes return valid ocean heights and even those can be impacted by errors from sea ice. Because the combined TOPEX/Poseidon, Jason-1, and Jason-2 time series is more than 23 years long, it is now possible to obtain sufficient data at crossover locations near Churchill to search for tidal changes. The satellites sense no changes in M₂ that are comparable to the changes seen at the Churchill gauge. The changes appear to be localized to the harbour, or to the Churchill River, or to the gauge itself.     

Validation of Sea Level Data in the East Asian Marginal Seas： Comparison between TOPEX／POSEIDON Altimeter and In-Situ Tide Gauges

In an effort to assess the reliability of satellite altimeter systems, the authors conduct a comparative analysis of sea level data that were collected from the TOPEX/POSEIDON (T/P) altimeter and 10 tide gauges (TG) near the satellite passing ground tracks. The analysis is made using datasets collected from marginal sea regions surrounding the Korean Peninsula at T/P cycles of 2 to 230, which correspond to October 1992 to December 1998. Proper treatment of tidal errors is a very critical step in data processing because the study area has very strong tide. When the T/P data are processed, the procedures of Park and Gamberoni (1995) are adapted to reduce errors associated with the tide. When the T/P data are processed in this way, the alias periods of M2, $2, and K1 constituents are found to be 62.1, 58.7, and 173 days repectively. The compatibility of the T/P and TG datasets are examined at various filtering periods.The results indicate that the low-frequency signals of the T/P data can be interpreted more safely with longer filtering periods (such as up to the maximum selected value of 200 days). When RMS errors for the 200-day low-pass filter period are compared with all 10 tidal stations, the values span the range of 2.8 to 6.7 cm. The results of a correlation analysis for this filtering period also show a strong agreement between the T/P and TG datasets across all stations investigated (e.g., p-values consistently less than 0.001). Hence according to the analysis, the conclusion is made that the analysis of surface sea level using satellite altimeter data can be made safely with reasonably extended filtering periods such as 200 days.     

由大尺度观测提取中尺度信息的可能性研究

利用浅水方程模式和变分四维同化方法对由大尺度观测提取中尺度信息的可能性进行了模拟试验研究。试验的初始场是在平直气流上叠加一个半径为 5倍格距的圆形涡旋。分别设定观测点的间距是 5 ,7和 9倍格距 ,观测的时间间隔分别是 1,2和 3h ,同化时间为 6h或 12h ,考察同化产生的初始场。试验结果是 :观测点的间距是 5倍格距时 ,由观测给出的分析场不能反映涡旋的基本特征 ,而在同化产生的初始场中 ,涡旋的基本结构清楚 ,但强度有所削弱。增加观测次数或者延长同化时间 ,可以改善同化的结果。对于移动较快的系统 ,同化的结果较好。当观测点的间距是 9倍格距时 ,同化的结果与分析场相比已无明显改进。     

Statistical Modeling and Trend Detection of Extreme Sea Level Records in the Pearl River Estuary

Sea level rise has become an important issue in global climate change studies. This study investigates trends in sea level records, particularly extreme records, in the Pearl River Estuary, using measurements from two tide gauge stations in Macau and Hong Kong. Extremes in the original sea level records(daily higher high water heights) and in tidal residuals with and without the 18.6-year nodal modulation are investigated separately. Thresholds for defining extreme sea levels are calibrated based on extreme value theory. Extreme events are then modeled by peaks-over-threshold models. The model applied to extremes in original sea level records does not include modeling of their durations, while a geometric distribution is added to model the duration of extremes in tidal residuals. Realistic modeling results are recommended in all stationary models. Parametric trends of extreme sea level records are then introduced to nonstationary models through a generalized linear model framework. The result shows that, in recent decades, since the 1960 s, no significant trends can be found in any type of extreme at any station, which may be related to a reduction in the influence of tropical cyclones in the region. For the longer-term record since the 1920 s at Macau, a regime shift of tidal amplitudes around the 1970 s may partially explain the diverse trend of extremes in original sea level records and tidal residuals.     

渤海西岸致灾风暴潮的统计预报模型

渤海西岸是风暴潮灾害多发区,1990年代以后发生几率和灾害损失明显增加。利用气象科学和海洋水文科学相结合的方法,依据黄骅港潮汐资料,对发生在渤海西岸的风暴潮进行统计分析。结果表明,台风和强冷空气配合气旋是造成渤海西岸风暴潮的主要天气系统,偏东大风增水和天文潮叠加是造成风暴潮的直接因素;风暴潮和天文潮汐都有半日潮现象。在此基础上,建立了渤海西岸风暴潮预报模型,通过台风或冷空气配合气旋影响时增水值的计算,结合天文潮汐资料,做出最高潮位预报。应用该预报方法对渤海西岸发生的7次风暴潮进行回报,预报值与实测值基本相当,是基层台站较实用的预报方法。     

bbGPS/PWV资料三维变分同化改进MM5降水预报连续试验的评估

利用区域地基GPS网反演的高时空密度的大气垂直方向水汽总量,也称为可降水量（PWV）,可大大弥补常规探空探测水汽资料的不足。为了全面评估区域GPS网PWV资料同化对业务数值天气预报改进程度的目的,在个例研究分析的基础上,进行了连续38天的GPS/PWV资料三维同化（3D-Var）改进数值业务预报的试验。研究方法是根据长江三角洲地区GPS气象网在2002年梅雨和盛夏季节观测的刖资料,通过三维变分同化建立中尺度数值预报模式MM5的初始场,逐日作出长江三角洲地区24小时的降水量预报。以6小时累积雨量为对象,与未同化GPS／刖资料的MM5的相应预报比较,通过多种评分方法,评估了GPS／PWV资料改进MM5降水预报的效果。结果表明GPS／PWV资料同化后的MM5降水预报能力在大部分时间和大部分地区都有所提高,主要是伪击率有较明显的下降,对小范围降水预报的改进更为明显。预报明显改进的区域恰好位于GPS站填补常规探空站间距较大的地区。     

2030年上海地区相对海平面变化趋势的研究和预测

从全球气候变化区域响应角度,依据1912-2000年吴淞验潮站年平均潮位资料,构建灰色线性回归组合模型,并将其与最小二乘法和小波变换相结合,分析以吴淞为代表的上海绝对海平面长期变化趋势和周期变化规律。由此预测2030年上海绝对海平面相对2011年的上升值为4 cm,结合已公布的构造沉降和城市地面沉降、流域水土保持和大型水利工程及人工挖沙导致的河口河槽冲刷、河口围海造地和深水航道及跨江跨海大桥导致水位抬升等叠加效应及其变化趋势,预测2030年上海市相对海平面上升10～16 cm,陆地海平面上升有7个风险分区。     

中国近海海平面变化趋势的对比分析

本文分析了近40年的中国近海验潮站资料海表面高度的线性变化趋势,并与卫星高度计资料进行了对比。通过对验潮站资料的分析发现,中国海域无论是近40年(1970~2013年)、还是近20年(1993~2013年)海平面均显著上升。各海区近20年的海平面上升有加速的趋势,且各时段上升速率大于全球平均海平面上升率。但是,受到海平面的年际和年代际变化的影响,近10年海平面上升趋势放缓。同时,本文也分析了不同季节海平面变化的趋势,北部海域秋季最大,冬季最小;南海海域春季最大,秋季最小。通过AVISO资料和验潮站资料的对比可以发现,AVISO资料在描述近20年海平面变化的线性趋势上与验潮站资料接近,较大的差异主要是由验潮站地表发生升降引起的。同时,通过对比也发现了用验潮站资料估算海域平均的海平面高度变化会有一定的误差,在黄海、渤海、东海海域验潮站估计的数值偏高,而在南海海域则偏低。     

Tides and Turbulent Mixing in the North of Taiwan Island

Microstructure and hydrological profiles were collected along two cross-shelf sections from the deep slope to the shallow water in the north of Taiwan Island in the summer of 2006. While the tidal currents on the shelf were dominated by the barotropic tide with the current ellipse stretched across the shelf, significant internal tides were observed on the slope. The depth-mean turbulent kinetic energy(TKE) dissipation rate on the shelf was 10~(-6)W kg-1, corresponding to a diapycnal diffusivity of 10~(-2)m~2s~(-1). The depth-mean TKE dissipation rate on the slope was 1 × 10~(-7)W kg-1, with diapycnal diffusivity of 3.4 × 10~(-4)m~2s~(-1). The shear instability associated with internal tides largely contributed to the TKE dissipation rate on the slope from the surface to 150 m, while the enhanced turbulence on the shelf was dominated by tidal or residual current dissipations caused by friction in the thick bottom boundary layer(BBL). In the BBL, the Ekman currents associated with the northeastward Taiwan Warm Current were identified, showing a near-bottom velocity spiral, which agreed well with the analytical bottom Ekman solution.     

青藏高原东缘GPS水汽资料对暴雨模拟的影响分析

选取2009年6月30日发生在云南南部和湖南北部的强降水过程,利用WRF模式和建立在青藏高原东缘地区18个地基GPS站点观测的可降水量资料（GPS/PWV）进行同化试验.试验表明：选取全部18个站和云南省8个站GPS/PWV资料进行同化,发现下游地区的强降水区湖南北部降水强度发生较大变化.选取100.E附近的6个站GPS/PWV资料进行同化,发现下游地区的强降水区湖南北部降水强度变化不大.利用全部站点GPS/PWV资料,模式初始场大部分地区湿度增加,对应下游降水中心强度增加,少部分地区湿度减少,对应降水区域南移.GPS/PWV资料同化对模式初始场湿度场和高度场影响较大,而对温度和风场影响较小.     

Simulation of heavy rainfall events over Indian monsoon region using WRF-3DVAR data assimilation system

We present the results of the impact of the 3D variational data assimilation (3DVAR) system within the Weather Research and Forecasting (WRF) model to simulate three heavy rainfall events (25–28 June 2005, 29–31 July 2004, and 7–9 August 2002) over the Indian monsoon region. For each event, two numerical experiments were performed. In the first experiment, namely the control simulation (CNTL), the low-resolution global analyses are used as the initial and boundary conditions of the model. In the second experiment (3DV-ANA), the model integration was carried out by inserting additional observations in the model’s initial conditions using the 3DVAR scheme. The 3DVAR used surface weather stations, buoy, ship, radiosonde/rawinsonde, and satellite (oceanic surface wind, cloud motion wind, and cloud top temperature) observations obtained from the India Meteorological Department (IMD). After the successful inclusion of additional observational data using the 3DVAR data assimilation technique, the resulting reanalysis was able to successfully reproduce the structure of convective organization as well as prominent synoptic features associated with the mid-tropospheric cyclones (MTC). The location and intensity of the MTC were better simulated in the 3DV-ANA as compared to the CNTL. The results demonstrate that the improved initial conditions of the mesoscale model using 3DVAR enhanced the location and amount of rainfall over the Indian monsoon region. Model verification and statistical skill were assessed with the help of available upper-air sounding data. The objective verification further highlighted the efficiency of the data assimilation system. The improvements in the 3DVAR run are uniformly better as compared to the CNTL run for all the three cases. The mesoscale 3DVAR data assimilation system is not operational in the weather forecasting centers in India and a significant finding in this study is that the assimilation of Indian conventional and non-conventional observation datasets into numerical weather forecast models can help improve the simulation accuracy of meso-convective activities over the Indian monsoon region. Results from the control experiments also highlight that weather and regional climate model simulations with coarse analysis have high uncertainty in simulating heavy rain events over the Indian monsoon region and assimilation approaches, such as the 3DVAR can help reduce this uncertainty.     

Variational data assimilation experiments of mei-yu front rainstorms in China

The numerical forecasts of mei-yu front rainstorms in China has been an important issue. The intensity and pattern of the frontal rainfall are greatly influenced by the initial fields of the numerical model. The 4-dimensional variational data assimilation technology (4DVAR) can effectively assimilate all kinds of observed data, including rainfall data at the observed stations, so that the initial fields and the precipitation forecast can both be greatly improved. The non-hydrostatic meso-scale model (MM5) and its adjoint model are used to study the development of the mei-yu front rainstorm from 1200 UTC 25 June to 0600 UTC 26 June 1999. By numerical simulation experiments and assimilation experiments, the T106 data and the observed 6-hour rainfall data are assimilated. The influences of many factors, such as the choice of the assimilated variables and the weighting coefficient, on the precipitation forecast results are studied. The numerical results show that 4DVAR is valuable and important to mei-yu front rainfall prediction.     

Oceanic tides over the Newfoundland and Scotian Shelves from TOPEX/POSEIDON altimetry

Abstract

A modified response analysis in the form of an orthotide parametrization is used to derive major semi‐diurnal and diurnal tidal constituents over the Newfoundland and Scotian Shelves from TOPEX/POSEIDON altimeter data. The orthotide formulation simultaneously solves for eight major semi‐diurnal and diurnal constituents, and has an accuracy of better than ～1.5 cm for each constituent. Tidal elevations are derived from the altimeter data on the ascending and descending satellite ground tracks, and interpolated using the method of statistical interpolation. The semi‐diurnal constituents (M₂, S₂ and N₂) compare favourably with available in‐situ observations and a numerical model. The diurnals (K₁ and O₁) are not as accurate as the semi‐diurnals, especially in the nearshore environment. The paper demonstrates the ability of TOPEX/POSEIDON altimetry to provide accurate tidal data over a continental shelf.     

Aerosol Data Assimilation Using Data from Fengyun-3A and MODIS:Application to a Dust Storm over East Asia in 2011

Aerosol optical depth(AOD) is the most basic parameter that describes the optical properties of atmospheric aerosols,and it can be used to indicate aerosol content. In this study, we assimilated AOD data from the Fengyun-3 A(FY-3 A) and MODIS meteorological satellite using the Gridpoint Statistical Interpolation three-dimensional variational data assimilation system. Experiments were conducted for a dust storm over East Asia in April 2011. Each 0600 UTC analysis initialized a24-h Weather Research and Forecasting with Chemistry model forecast. The results generally showed that the assimilation of satellite AOD observational data can significantly improve model aerosol mass prediction skills. The AOD distribution of the analysis field was closer to the observations of the satellite after assimilation of satellite AOD data. In addition, the analysis resulting from the experiment assimilating both FY-3 A/MERSI(Medium-resolution Spectral Imager) AOD data and MODIS AOD data had closer agreement with the ground-based values than the individual assimilation of the two datasets for the dust storm over East Asia. These results suggest that the Chinese FY-3 A satellite aerosol products can be effectively applied to numerical models and dust weather analysis.     

青藏高原坡面观测信息对我国夏季降水预报的作用

利用不同同化方式分别同化青藏高原地区新一代综合气象观测网的自动站和GPS大气可降水量信息,探讨这些观测资料对我国夏季不同区域降水预报的作用。通过两组数值试验对2008年夏季连续两个月的天气进行分析场和降水预报结果检验,得出以下主要结论：（1）由于同化测站的平均台站高度在2550m以上,因此同化青藏高原地区新一代综合气象观测网资料后,对背景场调整的正作用主要集中在500 hPa以上;循环同化方式对背景场的调整作用比静态同化方式更明显,尤其在500 hPa以上;（2）无论用静态同化,还是循环同化,该观测网资料对华北地区降水预报的改善作用都不太明显,只是对个别降水量级有改善作用;（3）采用静态同化,会对西南地区东部24小时降水预报有改善作用;在多数情况下同化沿99°E附近的7个测站资料得到的降水预报结果比同化24个站的好;（4）对于长江中下游地区,采用循环同化方式更有利于该地区降水预报准确率的提高,尤其是对25～48小时降水的预报;同时,在多数情况下同化24个自动站和GPS大气可降水量信息对降水预报改善比只同化7个站的更好。     

时间加密探空观测对分析和预报质量的敏感性研究

探空观测是气象资料同化中最基本的常规观测资料,对同化分析和预报的有效改善具有重要作用。由于现有探空观测站的空间分辨率较低,分布不均匀,且每日仅有两次观测,数量偏少,限制了其分析场对中小尺度大气状态的准确再现能力。自我国L波段雷达-数字探空仪更新换代以来,探空观测具备了获取每日4次、垂直分辨为秒级和分钟级的大气廓线资料。本文利用WRF中尺度数值模式,通过06时（世界时,下同）加密探空资料和12时常规探空资料的有效同化,研究分析了时间加密探空观测资料对同化分析和预报质量的敏感性影响。结果表明：同化06时的时间加密探空资料的午后暴雨预报质量优于12时常规探空观测。具体而言,同化06时的时间加密探空资料预报的大雨和暴雨的预报技巧高于12时常规探空资料;位势高度、温度和风场等预报场的均方根误差在高层的改进效果更加明显;06时的时间加密探空资料的同化对高层的高空急流和低层的水汽通量散度的预报质量贡献更大。批量试验进一步证实了有效同化时间加密探空资料对分析和数值预报效果改进的积极意义。     

南海温盐流数值产品构建及评估

基于区域海洋模式ROMS构造了一套覆盖中国南海的40年（1980—2019年）温盐流数值产品OCEAN＿SCS。OCEAN＿SCS的变量包含了温度、盐度、流速、流向以及海表高度。OCEAN＿SCS的水平空间分辨率为0.1°×0.1°,垂向分层40层（0～5 000 m）,时间分辨率为1小时,包含潮汐信息。利用独立的观测资料对OCEAN＿SCS进行了初步评估,评估对象包括温度、盐度、海表高度、海流、潮位和增水。在不包含资料同化的前提下,OCEAN＿SCS的模拟精度达到了较高的水准。OCENA＿SCS的构建将为南海海洋环境的研究提供数据支撑,并服务于南海海洋环境保障。