背景误差相关结构的统计分析与Envisat ASAR海浪谱资料同化研究
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摘要
海浪资料同化能够改进海浪的模拟和预报水平,影响海浪同化效果的重要因素是观测资料的选择和背景误差协方差矩阵(或背景误差相关函数矩阵)的表达。本文提出了一种新的背景误差构造方法,开展了有效波高背景误差相关结构的统计分析和参数化拟合研究;实现了Envisat ASAR海浪谱资料的最优插值同化,提出了两种各向异性的背景误差相关函数,开展了多种情形下的海浪谱同化实验并比较它们的同化效果。
首先,基于第三代海浪数值模式LAGFD-WAM,将间隔24小时的有效波高预报之差作为有效波高背景误差的近似。基于模式预报的时间序列,构造了有效波高背景误差的时间序列,进而得到有效波高的误差协方差矩阵和背景误差相关函数,统计和分析了有效波高背景误差的相关结构。结果表明,有效波高背景误差是各向异性和非均质的。提出了4种解析形式的椭圆形状各向异性背景误差相关函数,给出了椭圆三个参数的拟合结果,讨论了预报间隔对有效波高背景误差结构统计的影响。
其次,为了评估本文所用的海浪谱资料,对2003年至2008年的Envisat ASAR波模式海浪谱产品作了数据筛选和质量控制,并与太平洋海域的浮标实测资料进行了比对分析。结果表明:(1)ASAR一维频率谱的谱形测量较准,但谱值大小差异较大,频率谱的低频部分与浮标实测吻合更好;(2)ASAR有效波高比浮标实测略低,两者的均值偏差为-0.05m,均方根偏差为0.62m(3)ASAR平均周期比浮标实测偏高,两者的均值偏差为0.97秒,均方根偏差为1.42秒。
最后,开展了多种情形下的海浪同化实验。主要结论是:(1)传统的四种各向同性背景误差相关函数的同化效果相差不大,关键仍是对相关距离尺度的选取;相同相关距离尺度下的不同背景误差相关函数,可近似等效成不同相关距离尺度下的某一种背景误差相关函数。(2)存在最优的背景误差相关距离尺度,针对自回归形式的背景误差相关函数,本文结果表明相关距离尺度量级取400km至500km时同化效果最好,此时同化后的模式有效波高均方根误差比未同化时减小了26.0%。(3)各向异性背景误差相关函数的同化效果优于传统的各向同性误差相关函数;基于模式预报输出统计得到的“原始”各向异性背景误差相关函数的同化效果最好,椭圆形状各向异性的背景误差相关函数的同化效果次之,传统的各向同性背景误差相关函数的同化效果相对最差,它们使同化后的模式有效波高均方根误差比未同化时分别减小了26.4%、24.5%和23.4%。(4)同化实验表明波谱资料的最优插值同化效果优于单纯的有效波高资料最优插值。
Ocean wave data assimilation can improve the simulation and forecast level of the realistic wave field. The key factors influencing wave data assimilation effects are the choice of observation data and the presentation of background error covariance matrix (or background error correlation function). One new method to construct the background errors was given. The statistical analysis and parameteration of the correlation structure of significant wave height (SWH) background error were studied. The optimal interpolation (OI) assimilation of Envisat ASAR ocean wave data was carried out. And two different anisotropic background error correlation functions were presented. Finally, several groups of assimilation experiments under different settings were run to check their assimilation effects.
Firstly, based on the third-generation wave model named LAGFD-WAM, the difference between the SWH forecasts with 24 hours interval is considered as the approximation of SWH background errors. The time series of SWH background errors were constructed from the time series of the wave model forecasts. And the background error covariance matrices and the background error correlation function matrices were also constructed. Then the correlation structure of SWH background errors was statistically analyzed. The results indicated that the SWH background error is anisotropic and inhomogeneous. Hence, four different ellipse-type anisotropic analytic forms of background error correlation functions were presented. The three parameters of error ellipses were fitted. And the influence of the forecast interval on the background error structure statistic was discussed too.
Secondly, Envisat ASAR wave mode ocean wave spectra products from year 2003 to 2008 which had been filtered and quality-controlled were compared with buoy observation data in Pacific in order to assess the wave spectra data. The results show that: (1) ASAR one-dimensional frequency spectra agree well with buoy observations in spectral shapes and bad in spectral values. The agreement in the low frequency domain is better than that in high frequency domain. (2) ASAR SWH is a little lower than SWH of buoy observations. The mean bias of SWH is -0.05m and the root mean square (RMS) error is 0.62m. (3) The mean wave period of ASAR is higher than that of buoy observations. The mean bias is 0.97s and RMS error is 1.42s.
Finally, several ocean wave assimilation experiments under different situations and settings were run. The main conclusions are that (1) the difference of assimilation effects among traditional four isotropic background error correlation functions is not obvious and the key is still the choice of the correlation length scale. Different background error correlation functions under the same background error correlation length scale can be approximated by the one background error correlation function under different correlation length scales. (2) The optimal background error correlation length scale exists. For the auto-regressive background error correlation function, the assimilation effect is found to be best when the correlation length scale is assumed to be from 400km to 500km. And the modeled SWH RMS error reduced relatively 26% than that with no data assimilation in the best case. (3) The assimilation effect of anisotropic background error correlation functions is better than that of isotropic background error correlation functions. The effect of the experiment with the original anisotropic background error correlation function from wave model output statistics is the best, followed by the experiment with the ellipse-type anisotropic background error correlation function, and the last is the experiment with the traditional isotropic background error correlation function. The SWH RMS errors reduced relatively 26.4%, 24.5% and 23.4% respectively than that with no data assimilation in these three cases. (4) The assimilation experiment here also showed that assimilation effect of the wave spectra data OI was better than the only SWH OI.
首先,基于第三代海浪数值模式LAGFD-WAM,将间隔24小时的有效波高预报之差作为有效波高背景误差的近似。基于模式预报的时间序列,构造了有效波高背景误差的时间序列,进而得到有效波高的误差协方差矩阵和背景误差相关函数,统计和分析了有效波高背景误差的相关结构。结果表明,有效波高背景误差是各向异性和非均质的。提出了4种解析形式的椭圆形状各向异性背景误差相关函数,给出了椭圆三个参数的拟合结果,讨论了预报间隔对有效波高背景误差结构统计的影响。
其次,为了评估本文所用的海浪谱资料,对2003年至2008年的Envisat ASAR波模式海浪谱产品作了数据筛选和质量控制,并与太平洋海域的浮标实测资料进行了比对分析。结果表明:(1)ASAR一维频率谱的谱形测量较准,但谱值大小差异较大,频率谱的低频部分与浮标实测吻合更好;(2)ASAR有效波高比浮标实测略低,两者的均值偏差为-0.05m,均方根偏差为0.62m(3)ASAR平均周期比浮标实测偏高,两者的均值偏差为0.97秒,均方根偏差为1.42秒。
最后,开展了多种情形下的海浪同化实验。主要结论是:(1)传统的四种各向同性背景误差相关函数的同化效果相差不大,关键仍是对相关距离尺度的选取;相同相关距离尺度下的不同背景误差相关函数,可近似等效成不同相关距离尺度下的某一种背景误差相关函数。(2)存在最优的背景误差相关距离尺度,针对自回归形式的背景误差相关函数,本文结果表明相关距离尺度量级取400km至500km时同化效果最好,此时同化后的模式有效波高均方根误差比未同化时减小了26.0%。(3)各向异性背景误差相关函数的同化效果优于传统的各向同性误差相关函数;基于模式预报输出统计得到的“原始”各向异性背景误差相关函数的同化效果最好,椭圆形状各向异性的背景误差相关函数的同化效果次之,传统的各向同性背景误差相关函数的同化效果相对最差,它们使同化后的模式有效波高均方根误差比未同化时分别减小了26.4%、24.5%和23.4%。(4)同化实验表明波谱资料的最优插值同化效果优于单纯的有效波高资料最优插值。
Ocean wave data assimilation can improve the simulation and forecast level of the realistic wave field. The key factors influencing wave data assimilation effects are the choice of observation data and the presentation of background error covariance matrix (or background error correlation function). One new method to construct the background errors was given. The statistical analysis and parameteration of the correlation structure of significant wave height (SWH) background error were studied. The optimal interpolation (OI) assimilation of Envisat ASAR ocean wave data was carried out. And two different anisotropic background error correlation functions were presented. Finally, several groups of assimilation experiments under different settings were run to check their assimilation effects.
Firstly, based on the third-generation wave model named LAGFD-WAM, the difference between the SWH forecasts with 24 hours interval is considered as the approximation of SWH background errors. The time series of SWH background errors were constructed from the time series of the wave model forecasts. And the background error covariance matrices and the background error correlation function matrices were also constructed. Then the correlation structure of SWH background errors was statistically analyzed. The results indicated that the SWH background error is anisotropic and inhomogeneous. Hence, four different ellipse-type anisotropic analytic forms of background error correlation functions were presented. The three parameters of error ellipses were fitted. And the influence of the forecast interval on the background error structure statistic was discussed too.
Secondly, Envisat ASAR wave mode ocean wave spectra products from year 2003 to 2008 which had been filtered and quality-controlled were compared with buoy observation data in Pacific in order to assess the wave spectra data. The results show that: (1) ASAR one-dimensional frequency spectra agree well with buoy observations in spectral shapes and bad in spectral values. The agreement in the low frequency domain is better than that in high frequency domain. (2) ASAR SWH is a little lower than SWH of buoy observations. The mean bias of SWH is -0.05m and the root mean square (RMS) error is 0.62m. (3) The mean wave period of ASAR is higher than that of buoy observations. The mean bias is 0.97s and RMS error is 1.42s.
Finally, several ocean wave assimilation experiments under different situations and settings were run. The main conclusions are that (1) the difference of assimilation effects among traditional four isotropic background error correlation functions is not obvious and the key is still the choice of the correlation length scale. Different background error correlation functions under the same background error correlation length scale can be approximated by the one background error correlation function under different correlation length scales. (2) The optimal background error correlation length scale exists. For the auto-regressive background error correlation function, the assimilation effect is found to be best when the correlation length scale is assumed to be from 400km to 500km. And the modeled SWH RMS error reduced relatively 26% than that with no data assimilation in the best case. (3) The assimilation effect of anisotropic background error correlation functions is better than that of isotropic background error correlation functions. The effect of the experiment with the original anisotropic background error correlation function from wave model output statistics is the best, followed by the experiment with the ellipse-type anisotropic background error correlation function, and the last is the experiment with the traditional isotropic background error correlation function. The SWH RMS errors reduced relatively 26.4%, 24.5% and 23.4% respectively than that with no data assimilation in these three cases. (4) The assimilation experiment here also showed that assimilation effect of the wave spectra data OI was better than the only SWH OI.
引文
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