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参考文献 17
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目录 contents

    摘要

    高光谱大气红外探测器(Atmospheric Infrared Sounder,AIRS)主要覆盖CO2H2O吸收带光谱区。区别于CO2通道,H2O通道亮温偏差非高斯性较强。为了充分有效地利用AIRS通道光谱信息,本文采用两种新算法开展应用研究,一是基于变分同化后验估计-观测误差重估计重新估算光谱通道误差,以更好地“符合”光谱亮温对变分同化目标泛函的权值分配;二是将M—估计法(L2—估计、Huber—估计、Fair—估计和Cauchy—估计)权重函数耦合到经典变分同化目标泛函中,得到广义变分同化目标泛函,使其具有非高斯性,其核心是在每次极小化迭代过程中重新估计观测项对目标泛函贡献率。在新算法研究基础上开展高光谱AIRS模拟亮温试验,结果表明观测误差重估计和Huber—估计广义变分同化AIRS资料效果优于经典变分同化。并基于信号自由度(Degrees of freedom for signal,DFS)开展观测资料对分析场影响诊断,得到该两种方法在同化过程中能够提高H2O通道亮温使用的信息量。通过对文中算法(观测误差重估计和Huber—估计)得到的分析场与探空资料温度场对比分析,得到Huber-估计广义尺度设定为1.345 K时效果最好,整体误差最小,2.5K次之,且观测误差重估计也优于经典变分同化结果。200~750 hPa效果较为显著,基于Huber-估计广义同化在对流层顶表面和周围(80~200 hPa)温度反演小于2 K。研究结果可为我国风云四号A星和风云三号D星高光谱资料变分同化提供新的方法思路和技术支撑。

    Abstract

    Hyper-spectral Atmospheric Infrared Sounder (AIRS) mainly covers the CO2 and H2O absorption bands. Different from CO2 channels, the brightness temperature bias of water vapor channel follows non-Gaussian statistics. In order to use AIRS channel spectral information effectively, new algorithm research is needed, two methods are presented in this paper: (1)Different from the observation error of the given spectral channel remains unchanged during the classical variational assimilation minimization iteration, the paper based on the posterior estimate of variational assimilation, namely, observation error re-estimation, re-estimating the channel observation error, which is then regarded as the weight of observation to the objective function of classical variational assimilation; Observation error re-estimation can be used to identify the reasonable observation errors which can fit variational assimilation model better. By using the weight function of M-estimators (L2-estimator, Huber-estimator, Fair-estimator and Cauchy-estimator) to couple the classical variational assimilation, and then obtain the generalized variational assimilation, make it Non-Gaussian. Re-estimated the contribution rate of observation terms to the objective function during each minimization iteration. The simulated brightness temperatures of AIRS are used to conduct ideal experiments. It is show that two methods of observation error re-estimation and Huber-estimator can provide better results than the classical method. We diagnose the impact of observations on the analysis with degrees of freedom for signal (DFS). The result of diagnosis shows that two methods can increase the available information of brightness temperatures of water vapour channels during the assimilation process. Furthermore, the analysis field obtained by using the algorithm (observation error re-estimation and Huber-estimator) in this paper is compared with the temperature field of sounding data, and it is obtained that the Huber-estimator, which generalized scale is set as 1.345 K with the best effect, which is set as 2.5 K latter, and the observation error re-estimation is better than classical variational assimilation. The effect of 200~750 hPa was relatively significant. The retrieval temperature at the surface and around the tropopause (80~200 hPa)is less than 2 K based on Huber-estimator variational assimilation. The results of this paper can lay the theoretical foundation and provide the algorithm reference for the variational assimilation of hyper-spectral data of Feng-Yun 4A and Feng-Yun 3D satellite.

  • 引言

    随着卫星探测技术和资料同化算法的发展,卫星探测资料对数值天气预报正效果的影响日益增加。在不同类型卫星探测资料中,高光谱大气红外探测资料包含丰富大气温度和水汽垂直结构信息,故其重要性尤为显著。搭载在地球观测系统(Earth Observing System,EOS)第二颗卫星Aqua的高光谱大气红外探测器(Atmospheric Infrared Sounder,AIRS),采用红外分光技术覆盖650~2700 cm-1红外光谱区域,2378个通道主要覆盖长波CO2H2O和短波CO2吸收[1]。高光谱AIRS亮温通过变分同化或反演能够得到精细的大气温度和湿度廓线等信[2]

    误差(“误差”从数理统计角度出发)服从高斯分布是经典变分同化假定之[3,4],当实际观测资料包含离群值时,误差将不服从高斯分布,具有“拖尾现象”。在变分同化时,如果资料存在离群值,则变分同化得到的最优参数估计结果不太理想,故需对进入变分同化系统的AIRS资料进行质量控[4]。但有些所谓的“离群值”代表了一些特殊天气现象或极端天气过程,如将其剔除则会丢失很多有用信[5]

    在给定高光谱AIRS通道最优组合后,通道观测误差的设定尤为重要。目前通用的经典变分同化,在变分极小化迭代过程中,通道观测误差给定后一般保持不变。Bormann等研[6]得出在卫星通道亮温云区同化时通道间呈较强相关性,为了度量通道间的相关性,其在文献中采用了Desroziers等提出的观测误差重估计方[7]。本文也是基于此方法进行高光谱AIRS误差重估计。

    国内外学者关于卫星探测器CO2光谱通道变分同化研究较[8]。考虑到高光谱AIRS水汽通道亮温不仅可以提供更多湿度信息,且对温度信息起补充作用。水汽通道亮温与模式湿度变量存在非线性关系,微小扰动湿度变量会导致较大亮温偏差(偏差定义为“观测值—模拟值”,即,O—B,此处“偏差”从卫星资料特有定义出发),从而使水汽通道亮温偏差呈现较强非高斯性。目前卫星水汽通道亮温变分同化研究工作较少,已有Smith等同化了垂直探测器(TIROS Operational Vertical Sounder,TOVS)的水汽通道、AMSU(Advanced Microwave Sounding Unit)—B的微波湿度计和MHS(Microwave Humidity Sensors)资料,改善了数值天气预报分析和预报模型湿度[9];James等基于较严格的“阈值法”开展了高光谱AIRS水汽通道资料在NCEP(National Centers for Environmental Prediction)全球预报系统的同化研究,得出了水汽通道同化难点归因于水汽通道亮温与模式变量非线性关系和雅克比Jacobian矩阵非线性等,使得变分同化目标泛函迭代中存在水汽通道亮温偏差周期性波动,导致极小化迭代收敛较慢或不收[10]。Fowler等在其文献中指出实际观测资料服从非高斯分布,且开展了非高斯观测误差对变分同化影响的研[11]。为了充分有效利用AIRS光谱通道信息,需进行非高斯H2O和云较敏感CO2通道变分同化新算法构建与应用研究。

    Wang 和Zhang基于广义变分开展了高光谱AIRS受云影响资料非高斯同化研究,本文在其方法基础上,将变分同化后验估计-观测误差重估计用于优化经典变分同化开展AIRS通道亮温同化研[3,7]。在广义变分同化基础上,基于信号自由度(Degrees of freedom for signal,DFS[5]“挖掘”文中采用方法的优势,开展高光谱AIRS理想同化试验。从AIRS实际观测出发,将文中算法得到的分析场与探空资料温度场进行对比分析。

  • 1 广义变分同化理论与观测误差重估计方法

    资料变分同化根据“最优”数理统计方法,利用一切可获取且可用的信息(如常规、非常规观测资料、大气运动物理规律等)与初猜场(也称背景场)进行有效融合,尽可能准确地估计某一时刻的大气状态,为数值天气预报提供更好的初值(也称分析场 [12]

  • 1.1 广义变分同化理论

    水汽通道亮温与状态变量之间非线性较强,水汽通道亮温偏差服从非高斯分[13,14]。广义变分同化能够同时兼顾偏差高斯和非高斯的特征,定义[3,5]

    Jx,w=12x-xbTB-1x-xb+12Hx-yoTwrR-1Hx-yo
    (1)

    其中,x是控制变量;xb是背景场;BR分别是背景和观测误差协方差矩阵;w(r)是权重因子,作为观测资料对目标泛函的贡献率;上标 -1T分别表示矩阵求逆和转置标记;yo是卫星通道观测亮温(即,通过普朗克方程遥感波段直接估算的亮温);H是观测算子,实现模式空间变量到观测空间投影映射。本文H采用Tiros业务垂直探测器辐射传输模式(Radiative Transfer for Tirosn Operational Vertical Sounder,RTTOV)模拟高光谱AIRS亮[15]

    w(r)=1rdρ(r)dr
    (2)

    其中,ρ(r)是M—估计代价函数,本文采用Huber—估计、Fair—估计、Cauchy—估计和L2-估计(即经典变分同化[3,5]d是求导标记;w(r)是对角矩阵,元素为w(ri)ri=yi-Hi(x)/σiyiHi(x)分别表示通道i的观测和模拟亮温;σi是观测误差;权重因子w具有自适应“调节”功能,当偏差超过M—估计“广义尺度”[3],减小通道亮温对目标泛函的影响,当偏差无限大时(+),则抑制通道亮温对目标泛函的影响,从数理统计角度出发,w的作用是降低“小概率”数据对变分同化结果的影响。权重因子w(r)在广义变分目标泛函极小化迭代过程中动态更新,动态重估观测项对目标泛函的贡献率,而经典变分同化w(r)始终为常数1。这也是本文采用方法优于经典变分同化的关键点。

    在广义变分同化中,M—估计权重函数的选取对观测项贡献率重估计至关重要。对于Huber—估计广义变分,当观测模拟亮温偏差较小且在广义尺度范围内,则有w(r)=1,即此时等价于经典变分同化方法,能够较好地变分同化亮温偏差高斯分布资料;当观测模拟亮温偏差较大,且在广义尺度范围外,则有w(r)1,即采用广义变分同化法,此时对H2O通道亮温变分同化效果显著(见本文试验部分)。

  • 1.2 变分同化后验估计-观测误差重估计方法

    本文基于Desroziers等提出的方[7]对高光谱AIRS通道观测误差进行重估计。该方法基于经典变分同化(L2—估计)服从线性估计理论的假设。背景亮温偏差db(O-B,B为背景场模拟亮温)定义为观测算子将背景场映射到观测空间时的观测与模拟的差值。

    db=yo-Hxb
    (3)

    用式(1)计算得到的分析场代替背景场(此时式(1)采用L2—估计),得到分析亮温偏差da(O-A,A为同化后的分析场模拟亮温):

    da=yo-Hxayo-Hxb-HKdb
    (4)

    基于误差无偏、背景和观测误差不相关、分析中观测值权值分配与真实误差协方差近似的假设,在观测空间中有:

    Rre=EdadbT
    (5)

    其中,E是数学期望值;Rre为重估计后的高光谱AIRS观测误[6,7,16]

    在观测误差重估计中,Hxa较为关键。它包含了辐射传输模型所使用的信息,如变分同化中Jacobian矩阵和求解过程中泰勒一阶近似等信息,通过此方法可以界定出“合理”的观测误差,以更“适应”变分同化模[10]

  • 2 高光谱AIRS模拟亮温广义和误差重估计变分同化试验

  • 2.1 相关模型介绍

    文中使用辐射传输模式RTTOV[15](网址:https://www.nwpsaf.eu/site/software/rttov/)和变分同化系统两个模型。变分同化模型在欧洲数值天气预报卫星应用设施(Numerical Weather Prediction Satellite Application Facility,NWP SAF)小组研发的一维变分(1DVar)系统基础上(网址:https://nwpsaf.eu/site/)作如下修改:

    (1)只考虑“模式空间”温度、湿度、气候态O3廓线和10 mU、10 mV风场、地表气压、温度和湿度信息。

    (2)改写经典变分同化目标泛函和相应梯度,添加M—估计(L2—估计、Huber—估计、Fair—估计和Cauchy—估计)广义变分同化代码。

    (3)加入观测误差重估计程序接口,以实现过程中需满足“广义”勾股定理成立条[7]

  • 2.2 理想试验数据

  • 2.2.1 高光谱AIRS最优通道组合介绍

    文中基于经典、误差重估计和M-估计广义变分开展高光谱AIRS模拟亮温同化理想试验。由于AIRS不同通道组合得到的最终变分同化或反演效果不同,因此在通道最优选择时,需建立通道黑名单,剔除仪器噪声、RTTOV 模拟误差较大和其它需要剔除的通,19],再对剩余通道采用目前主流的“熵减法”或其它改进方法进行选[20]。文中参考Joiner等学者的工作,选取AIRS 281个通[17],基于美国标准大气廓线采用辐射传输模式RTTOV计算得到的模拟亮温分布见图1(“下三角形”表示)。

    图1
                            高光谱AIRS光谱和理想试验所用通道分布(通道组合参考文献[17]Joiner等的研究成果)

    图1 高光谱AIRS光谱和理想试验所用通道分布(通道组合参考文献[17]Joiner等的研究成果)

    Fig.1 Distribution of spectrum and channels used in the ideal experimental of hyper-spectral AIRS(Channel combination reference Research results Literature [17] of Joiner et al)

    图1可以看出,该281个通道主要涵盖了长波CO2H2O、短波CO2和地表光谱区域。在进行广义变分和误差重估计理想试验研究时,该通道组合具有较好的代表性。

  • 2.2.2 变分同化背景场廓线和观测亮温介绍

    在变分同化分析中,背景廓线的引入至关重要。实际业务数值变分同化时,背景场通过数值天气模式循环同化预报或其它方式得到。本文借鉴Fowler[14]、Pavelind[18]和Noh[20]学者的研究方法开展算法应用研究,选取1DVar自带廓线集中的廓线作为本文研究的“真实”温度和湿度廓线,相应的RTTOV模拟亮温作为“真实”亮温。“真实”温度和湿度廓线通过添加高斯随机误差作为背景廓线。

    与CO2通道亮温偏差相比, H2O通道亮温偏差服从较强非高斯分布(图略),结合H2O和CO2通道固有特[21,22],对H2O和CO2通道“真实”亮温分别加入拉普拉斯和高斯随机误差扰动后的亮温作为观测亮温,则有:

    y=Hxt+εoR1/2
    (6)

    其中, yHxt分别为观测亮温和真实廓线模拟得到的“真实”亮温;εo为高斯和拉普拉斯随机数,拉普拉斯随机数由高斯随机数变换得到;R为观测误差协方差矩阵。

    需要说明的是:文中背景误差协方差B和高光谱AIRS通道原始观测误差R参考NWP SAF 1DVar(网址:https://nwpsaf.eu/site/)软件包中给定的[20]

  • 2.3 基于变分同化后验估计-高光谱AIRS通道观测误差重估计分析

    选取上述具有较好代表性的高光谱AIRS 281个通道进一步开展算法应用研究(见图2)。图2左分别给出了基于文中式(3)、(4)和(5)采用变分同化后验估计方法统计100和2000个样本得到的281个通道重估计观测误差分布,其中蓝线为高光谱AIRS通道原始观测误差;红线和绿线分别为统计100和2000个样本重估计后的观测误差。图2右为基于Huber—估计的广义变分同化在极小化初始迭代前计算的各个通道对变分同化目标泛函的权值分配。

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    图2 高光谱AIRS通道观测误差重估计和Huber权值分配

    Fig.2 Re-estimated hyper-spectral AIRS channel observation error (left) and weight estimates of Huber-estimator (right)

    图2左可以看出,高光谱AIRS的CO2光谱吸收带(中心波长在15.5 和 4.3 µm)通道重估计观测误差较原始观测误差有所降低,说明变分同化后验重估计增加了CO2吸收带通道亮温对目标泛函贡献率。H2O吸收带(中心波长在6.3 µm)通道重估计误差变大,说明重估计后降低了水汽通道亮温对目标泛函贡献率。从图2右也可以看出在目标泛函极小化初始迭代前水汽光谱带通道亮温偏差较大,非高斯较强,分配了较小权值,这与左图水汽通道误差重估计有较好的一致性。但观测误差重估计后,高光谱AIRS一些地表敏感通道(中心波长4.0 µm)观测误差显著减少可能与前期处理背景廓线时只扰动温度和湿度廓线有关,后期需进一步深入研 [3]

  • 2.4 理想试验变分同化效果对比分析及观测资料对分析场影响诊断研究

  • 2.4.1 变分同化效果分析比较

    因采用100和2000个样本观测误差重估计得到的高光谱AIRS通道误差值接近,因此本文只给出了100条廓线统计情况。变分同化高光谱AIRS 281个通道,给出了模式和观测空间均方根误差(Root—Mean—Square,RMS)。图3中给出了不同变分同化方法反演亮温、温度和湿度误差RMS。

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    注:图3高光谱AIRS 通道亮温(单位:K)、温度(单位:K)和湿度误差(单位:g/kg)RMS统计

    Fig.3 Brightness temperature (BT) of hyper-spectral AIRS (unit: K), temperature (unit: K) and humidity (unit: g/kg) error RMS statistics

    图3可以看出,基于Huber—估计的亮温变分同化效果最好,除水汽吸收处有些通道的亮温反演效果较差外,观测误差重估计优于经典变分同化;对于温度和湿度反演,也是基于Huber—估计的广义变分同化效果最好,尤其在水汽吸收带(见图3椭圆标记),观测误差重估计效果其次。Fair和Cauchy—估计效果较差,可能与其代价函数分布固有特点有[3]

    需要说明的是,本文估算亮温的方法为式(1)中的“x”经过极小化迭代得到的分析场“xa”在观测空间的映射“Hxa”,而通过普朗克方程遥感波段直接估算的亮温为公式(1)中的yo。变分同化的本质是在“模式空间”,使得到的xa(温度、湿度廓线等)与“真实大气”更接近;在“观测空间”,使得Hxa与真实观测yo更接近。

    分析原因:观测误差重估计利用经典变分同化(L2-估计)分析场和背景场通过观测算子投影到观测空间,基于线性估计理论,采用广义勾股定理得到。基于Huber—估计广义变分将通道亮温偏差较大通道对目标泛函贡献率赋予较小权值,而不是通过质量控制剔除或此次变分极小化迭代中不使用此亮温信息,这是与经典变分同化的主要区别,其能最大化有效地使用高光谱AIRS通道亮温信息,尤其非高斯性较强的水汽通道信息。

  • 2.4.2 M—估计权重因子作用分析-观测项对目标泛函贡献率动态重估计

    图4给出了本文理想试验条件下某条廓线在变分同化极小化迭代过程中AIRS通道亮温对目标泛函贡献率基于Huber和Fair—估计权函数的重估值。给出通道143(波数1040.15 cm-1)和通道200(波数1524.35 cm-1)极小化迭代过程中AIRS通道贡献率,迭代次数分别为185次和217次。迭代过程中当某通道贡献率低于25%时,则不使用此通道信息,但在后续迭代中该通道亮温可能被变分同化使用(图中灰线代表25%界限)。

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    图4 观测项对目标泛函贡献率动态重估计

    Fig.4 Dynamic re-estimation of the contribution rate of observation terms to the objective function

    图4可以看出,初始迭代中,由于高光谱AIRS通道观测模拟亮温偏差(O-B)较大,通道贡献率值较小,在后续迭代优化了背景廓线,其偏差(O-A)越来越“合理”。但从最终迭代可以得到,有些通道贡献率分配值还是较小。结合图3图4结论及原因分析可知,通道亮温有效同化特别是水汽通道同化算法的选取尤为关键。如采用经典变分同化,较多水汽通道信息因质量控制或误差高斯分布假定所剔除而无法进入变分同化系[10]

    为深入分析AIRS 281个通道在变分同化中如何被使用和较为客观评估每个通道相对作[20],本文基于信号自由度(Degrees of freedom for signal,DFS)采用高斯扰动和数值逼近方[5]开展通道亮温对分析场影响诊断。

    高光谱AIRS通道i的DFS影响率百分比DFS_Channeli定义为:

    DFS_Channeli=j=1100DFSi,ji=1281j=1100DFSi,j×100% ,
    (7)

    给出100条廓线中高光谱AIRS 281个通道的DFS影响率百分比(单位:%),见图5

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    Fig. 5 DFS effect rate percentages (unit: %) of the brightness temperatures of 281 AIRS channels to analysis field in different assimilation algorithms

    图5可以看出,高光谱AIRS 281个通道主要覆盖长波CO2H2O和短波CO2光谱带。因经典变分同化(L2—估计)服从误差高斯分布假定的局限性,因此更多地同化了长波CO2通道信息,而H2O通道进入信息量较少。在误差重估计中,因增大了H2O通道观测误差,降低了H2O通道亮温对目标泛函的贡献,故同化了较多的H2O通道。Huber—估计有效地“挖掘”水汽信息并进行了较好的变分同化使用。而Fair—估计和Cauchy—估计虽然同化了较多的水汽通道(图略),但由于其权重函数构建的局限[3],变分同化效果不太理想。

  • 3 变分同化高光谱AIRS亮温分析场与探空资料对比分析

  • 3.1 数据来源

    本文选取站点号为01415(经度:5.66,纬度:58.86)和02591(经度:18.35,纬度:57.65)两个探空站2014年8月1日至2014年8月31日累计一个月的探测资料。该探空资料来自于怀俄明大学网站(网址:http://weather.uwyo.edu/upperair/sounding.html)。统计过程中对AIRS和探空资料进行时空匹配,剔除探空缺测时次的AIRS资料。背景场采用NCEP的FNL分析场资料,水平和垂直方向分别采用双线性和取对数后线性插值将FNL资料插值到探空站点。

  • 3.2 变分同化试验设计

    本文主要对比分析经典变分同化(L2—估计)、变分同化后验估计-观测误差重估计和M—估计法(L2—估计、Huber—估计、Fair—估计和Cauchy—估计)广义变分同化效果,以分析广义变分同化方法的可行性。在前期高光谱AIRS理想试验基础上,选取观测误差重估计和Huber—估计广义变分同化开展对比试验,以验证其方法是否优于经典变分同化。试验设计如下:

    ①试验资料:被同化的高光谱AIRS观测和背景场资料均相同。

    ②试验平台:使用同样版本的辐射传输模式RTTOV和基于同样的变分同化系统。

    ③试验方法:在同一变分同化系统下设计对比试验(不同广义尺度的Huber—估计广义变分同化、观测误差重估计和经典变分同化),开展不同变分同化方法温度分析场与探空资料对比,以验证文中使用方法的可行性。

    ④资料处理:高光谱AIRS通道亮温匹配到探空资料时采用“最邻近法”;不考虑探空资料漂移现[20],对于探空资料垂直方向采用取对数后线性外插。

    ⑤通道组合:此同化试验在AIRS 281个通道组合基础上,选取了75个通道用于实际变分同化AIRS资料试验。

  • 3.3 变分同化结果分析

    图6分别给出了站点号01415和02591高光谱AIRS的75个通道观测亮温(O)、模拟亮温(B)和不同同化方法得到的分析场模拟亮温偏差绝对值平均。进一步给出相应时刻变分同化反演得到的温度场与探空资料各个模式气压层(RTTOV-43层,从0.1 hPa-1013.25 hPa)偏差绝对值平[20]。其中,“Huber2”和“Huber1”分别表示Huber—估计广义尺度设定为2.5 K和1.345 K[5];“L2”表示经典变分同化方法;“Reestimate”表示观测误差重估计;“Sounding”表示探空资料观测值。

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    Fig. 6 Comparison and analysis of high-spectral AIRS channel brightness temperature bias and temperature field with sounding data

    图6可知:①对于“通道亮温”,通道17(波数659.05 cm-1)、18(波数659.54 cm-1)、33(波数672.10 cm-1)和55(波数693.03 cm-1)变分同化后的通道亮温偏差增大,其它通道亮温偏差较小,且减小幅度显著。水汽通道70(波数1572.09cm-1)同化反演亮温与通道观测亮温接近,说明文中方法较好地同化了AIRS水汽通道亮温信息。地表通道71(波数2377.45 cm-1)的O-B绝对值均值较大,变分同化后显著减小。

    ②对于“温度廓线”,该资料统计时间段内探空站01415和02591顶层气压一般在17 hPa和27 hPa左右,高层探空温度廓线通过外插得到,故误差较大。从温度场与探空资料对比分析可知,Huber-估计广义尺度设定为1.345 K时(结合经验给定)效果最好,2.5 K次之,观测误差重估计也优于经典变分同化(L2-估计)。200~750 hPa效果较为显著,而在750 hPa以下接近,可能与FNL资料本身精度较高或此通道组合中只使用了部分地表通道有关。该结论与Noah等研究得到的相对湿度偏差变化趋势较为一[20]。有学[21]研究得出对流层顶表面和周围(80~200 hPa)温度反演精度仅为4 K的结论,而文中Huber-估计广义同化在此区域误差小于2K,但在200~300 hPa误差较大。因H2O通道被较好地同化使用(O-A偏差接近0),Huber-估计广义变分同化结果优于经典变分同化,尤其在对流层上层。

  • 4 总结与展望

    高光谱大气红外探测器AIRS通道信息量大,实际观测数据误差服从非高斯分布。本文在经典变分同化目标泛函中耦合误差重估计、Huber—估计广义变分同化AIRS,其结果优于经典变分同化。具体结论如下:

    (1)使用变分同化后验估计-观测误差重估计方法,降低了CO2通道观测误差,增加了H2O通道观测误差,使得H2O通道资料能被更合理地同化,重估观测误差包含了辐射传输模式信息,通过此方法可以界定出“合理”的光谱观测误差,与变分同化系统更“适应”。

    (2)基于信号自由度DFS进行高光谱AIRS通道亮温对分析场影响诊断,得到Huber—估计广义变分同化能够较好地进行H2O通道信息的合理使用,挖掘出“水汽”信息。

    (3)将观测误差重估计和Huber—估计得到的分析场与探空资料温度场进行对比分析,得到Huber-估计广义尺度设定为1.345 K时效果最好,2.5 K次之,观测误差重估计也优于经典变分同化。基于Huber-估计广义同化在对流层顶表面和周围(80~200 hPa)温度反演小于2 K,200~750 hPa效果较为显著。

    区别于Tavolato和Isaksen[22] 基于M—估计中的Huber—范数进行了温度、气压、湿度等观测资料的质量控制,本文对M—估计用于高光谱资料非高斯变分进行了有益的探索。在后续工作中,将进一步优化改进文中使用的新方法,根据不同数据特性基于M-估计代价函数基本性质构建新的M-估计法,并将广义变分同化的方法应用于我国自主研发的GRAPES(Global/Regional Assimilation and Prediction Enhanced System)模式开展实际个例应用研究,并进一步用于我国风云四号A星干涉式大气垂直探测仪(Geostationary Interferometric Infrared Sounder,GIIRS[23]和风云三号D星高光谱红外大气探测仪(Hyperspectral InfraRed Atmospheric Sounder,HIRAS[24]资料变分同化,以期提高降水落区、强度和台风路径预报。

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      Smith W L, Woolf H M, Hayden C M, et al. TIROS-N operational vertical sounder[J]. Bulletin of the American Meteorological Society, 1979, 60(10): 1177-1187.

    • 10

      James A J, John F L, Lars P. The Development of hyper-spectral infrared water vapor radiance assimilation techniques in the NCEP global forecast system. ECMWF/ EUMETSAT NWP-SAF Workshop on the assimilation of IASI in NWP, 6-8 8 May, 2009.

    • 11

      Fowler A, Leeuwen J. Observation impact in data assimilation: the effect of non-Gaussian observation error[J].Tellus A:Dynamic Meteorology and Oceanography, 2013, 65 (1), DOI: 10.3402.

    • 12

      WANG Gen, SHENG Shao-Xue, LIU Hui-Lan, et al. Discontinuous data 3D/4D variation fusion based on the constraint of L1 norm regularization term[J]. Advances in Earth Science,(王根,盛绍学,刘惠兰,等. 基于L1 范数正则项约束的不连续资料三维/ 四维变分融合研究.地球科学进展),2017,32(7):757-768.

    • 13

      Li J, Han W. A step forward toward effectively using hyperspectral IR sounding information in NWP[J]. Advances in Atmospheric Sciences, 2017, 34:1263-1264.

    • 14

      Fowler A. A sampling method for quantifying the information content of IASI channels [J]. Monthly Weather Review, 2017, 145(2):709-725.

    • 15

      Saunders R, Brunel P, English S, et al. RTTOV-8-Science and validation report. Eumetsat/ ECMWF SAF Programme, Document ID NWPSAF-MOTV-007. 2005,Available from: NWP SAF Helpdesk, Met Office, FitzRoy Road, Exeter, EX1 3PB, UK.

    • 16

      Waller J A, Ballard S P, Dance S L, et al. Diagnosing horizontal and inter-channel observation error correlations for SEVIRI observations using observation-minus-background and observation- minus-analysis statistics[J]. Remote Sensing, 2016, 8(7). 851. ISSN 2072-4292

    • 17

      Joiner J, Brin E, Treadon R, et al. Effects of data selection and error specification on the assimilation of AIRS data[J].Quarterly Journal of the Royal Meteorological Society, 2007,133 (622): 181-196.

    • 18

      Pavelin E G, English S J, Eyre J R. The assimilation of cloud affected infrared satellite radiances for numerical weather prediction[J]. Quarterly Journal of the Royal Meteorological Society, 2008,134 (632):737-749.

    • 19

      LIU Hui, DONG Chao-Hua, ZHANG Wen-Jian, et al. Retrieval of clear-air atmospheric temperature profiles using AIRS observation[J].Acta Meteorological Sinica,(刘辉,董超华,张文建,等.AIRS晴空大气温度廓线反演试验.气象学报),2008,66(4):513-519.

    • 20

      Noh Y, Sohn B, Kim Y, et al. A new infrared atmospheric sounding interferometer channel selection and assessment of its impact on Met Office NWP forecasts[J].Advances in Atmospheric Sciences, 2017, 34(11):1265-1281.

    • 21

      Arai K, Liang X. Sensitivity analysis for air temperature profile estimation methods around the tropopause using simulated Aqua/AIRS data [J]. Advances in Space Research, 2009, 43(1): 845-851.

    • 22

      Tavolato C, Isaksen L. On the use of a Huber norm for observation quality control in the ECMWF 4D-Var[J].Quarterly Journal of the Royal Meteorological Society, 2015,141(690): 1514-1527.

    • 23

      YANG Yu-Han, YIN Qiu, SHU Jiong. Channel selection of atmosphere vertical sounder (GIIRS) onboard the FY-4A geostationary satellite[J].Journal of Infrared and Millimeter Waves,(杨雨晗,尹球,束炯.FY-4A大气垂直探测仪 (GIIRS) 温度探测通道优选.红外与毫米波学报), 2018,37(5):545-552.

    • 24

      BAI Wen-Guang, ZHANG Peng, ZHANG Wen-Jian, et al. An efficient method for hyper-spectral infrared atmospheric radiation transfer calculation[J].Journal of Infrared and Millimeter Waves, (白文广,张鹏,张文建,等.一种高效计算高光谱分辨率红外大气辐射传输的方法.红外与毫米波学报),2016,35(1):99-108.

王根

机 构:

1. 安徽省气象信息中心 安徽省强天气集合分析和预报重点实验室,安徽 合肥 230031

2. 中国气象局沈阳大气环境研究所,辽宁 沈阳 110016

Affiliation:

1. Anhui Meteorological Information Centre Anhui Key Lab of Strong weather analysis and forecast, Hefei 230031, China

2. The Institute of Atmospheric Environment, China Meteorological Administration, Shenyang 110000, China

邮 箱:203wanggen@163.com

作者简介:(Biography):(Biography):王根(1983-),男,江苏泰州人,副高,博士学位,主要从事高光谱卫星资料同化、多源数据融合与深度学习等研究. E-mail:203wanggen@163.com

张正铨

机 构:中国科学技术大学数学学院,安徽 合肥 230022

Affiliation:School of Mathematics, University of Science and Technology of China, Heifei 230022,China

邓淑梅

机 构:安徽建筑大学 环境与能源工程学院,安徽 合肥 230601

Affiliation:School of Environment and Energy Engineering, Anhui Jianzhu University, Hefei 230601, China

刘惠兰

机 构:安徽省气象信息中心 安徽省强天气集合分析和预报重点实验室,安徽 合肥 230031

Affiliation:Anhui Meteorological Information Centre Anhui Key Lab of Strong weather analysis and forecast, Hefei 230031, China

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图1 高光谱AIRS光谱和理想试验所用通道分布(通道组合参考文献[17]Joiner等的研究成果)

Fig.1 Distribution of spectrum and channels used in the ideal experimental of hyper-spectral AIRS(Channel combination reference Research results Literature [17] of Joiner et al)

图2 高光谱AIRS通道观测误差重估计和Huber权值分配

Fig.2 Re-estimated hyper-spectral AIRS channel observation error (left) and weight estimates of Huber-estimator (right)

图2 高光谱AIRS通道观测误差重估计和Huber权值分配

Fig.2 Re-estimated hyper-spectral AIRS channel observation error (left) and weight estimates of Huber-estimator (right)

Fig.3 Brightness temperature (BT) of hyper-spectral AIRS (unit: K), temperature (unit: K) and humidity (unit: g/kg) error RMS statistics

Fig.3 Brightness temperature (BT) of hyper-spectral AIRS (unit: K), temperature (unit: K) and humidity (unit: g/kg) error RMS statistics

Fig.3 Brightness temperature (BT) of hyper-spectral AIRS (unit: K), temperature (unit: K) and humidity (unit: g/kg) error RMS statistics

图4 观测项对目标泛函贡献率动态重估计

Fig.4 Dynamic re-estimation of the contribution rate of observation terms to the objective function

图4 观测项对目标泛函贡献率动态重估计

Fig.4 Dynamic re-estimation of the contribution rate of observation terms to the objective function

图4 观测项对目标泛函贡献率动态重估计

Fig.4 Dynamic re-estimation of the contribution rate of observation terms to the objective function

图4 观测项对目标泛函贡献率动态重估计

Fig.4 Dynamic re-estimation of the contribution rate of observation terms to the objective function

Fig. 5 DFS effect rate percentages (unit: %) of the brightness temperatures of 281 AIRS channels to analysis field in different assimilation algorithms

Fig. 5 DFS effect rate percentages (unit: %) of the brightness temperatures of 281 AIRS channels to analysis field in different assimilation algorithms

Fig. 5 DFS effect rate percentages (unit: %) of the brightness temperatures of 281 AIRS channels to analysis field in different assimilation algorithms

Fig. 5 DFS effect rate percentages (unit: %) of the brightness temperatures of 281 AIRS channels to analysis field in different assimilation algorithms

Fig. 5 DFS effect rate percentages (unit: %) of the brightness temperatures of 281 AIRS channels to analysis field in different assimilation algorithms

Fig. 6 Comparison and analysis of high-spectral AIRS channel brightness temperature bias and temperature field with sounding data

Fig. 6 Comparison and analysis of high-spectral AIRS channel brightness temperature bias and temperature field with sounding data

Fig. 6 Comparison and analysis of high-spectral AIRS channel brightness temperature bias and temperature field with sounding data

Fig. 6 Comparison and analysis of high-spectral AIRS channel brightness temperature bias and temperature field with sounding data

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    • 2

      ZHAO Qiang, HAN Lu, YANG Shi-Zhi, et al. Retrieval of atmospheric profile by hyperspectral infrared satellite data[J].Journal of Atmospheric and Environmental Optics,(赵强,韩露,杨世植,等.利用超光谱红外卫星数据反演大气廓线研究.大气与环境光学学报), 2016, 11(2): 118-124.

    • 3

      Wang G, Zhang J W. Generalised variational assimilation of cloud-affected brightness temperature using simulated hyper-spectral atmospheric infrared sounder data[J]. Advances in Space Research, 2014, 54(1):49-58.

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      WANG Gen, ZHANG Hua, YANG Yin. Research progress of quality control for AIRS data[J]. Advances in Earth Science,(王根,张华,杨寅. 高光谱大气红外探测器AIRS 资料质量控制研究进展. 地球科学进展),2017,32(2):139-150.

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      WANG Gen, TANG Fei, LIU Xiao-Bei, et al. Application of M-estimators method on FY-3B/IRAS channel brightness temperature generalized variational assimilation[J]. Journal of Remote Sensing, (王根, 唐飞, 刘晓蓓,等. M-估计法广义变分同化FY-3B/IRAS通道亮温.遥感学报),2017, 21(1): 52-61.

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      Bormann N, Geer A J, Bauer P. Estimates of observation-error characteristics in clear and cloudy regions for microwave imager radiances from numerical weather prediction[J]. Quarterly Journal of the Royal Meteorological Society, 2011, 137(661): 2014-2023.

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      Desroziers G, Berre L, Chapnik B. Diagnosis of observation, background and analysis-error statistics in observation space [J]. Quarterly Journal of the Royal Meteorological Society, 2005, 131(613): 3385-3396.

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      McNally A P, Watts P D, Smith J, et al. The assimilation of AIRS radiance data at ECMWF[J]. Quarterly Journal of the Royal Meteorological Society, 2006, 132(616): 935-957.

    • 9

      Smith W L, Woolf H M, Hayden C M, et al. TIROS-N operational vertical sounder[J]. Bulletin of the American Meteorological Society, 1979, 60(10): 1177-1187.

    • 10

      James A J, John F L, Lars P. The Development of hyper-spectral infrared water vapor radiance assimilation techniques in the NCEP global forecast system. ECMWF/ EUMETSAT NWP-SAF Workshop on the assimilation of IASI in NWP, 6-8 8 May, 2009.

    • 11

      Fowler A, Leeuwen J. Observation impact in data assimilation: the effect of non-Gaussian observation error[J].Tellus A:Dynamic Meteorology and Oceanography, 2013, 65 (1), DOI: 10.3402.

    • 12

      WANG Gen, SHENG Shao-Xue, LIU Hui-Lan, et al. Discontinuous data 3D/4D variation fusion based on the constraint of L1 norm regularization term[J]. Advances in Earth Science,(王根,盛绍学,刘惠兰,等. 基于L1 范数正则项约束的不连续资料三维/ 四维变分融合研究.地球科学进展),2017,32(7):757-768.

    • 13

      Li J, Han W. A step forward toward effectively using hyperspectral IR sounding information in NWP[J]. Advances in Atmospheric Sciences, 2017, 34:1263-1264.

    • 14

      Fowler A. A sampling method for quantifying the information content of IASI channels [J]. Monthly Weather Review, 2017, 145(2):709-725.

    • 15

      Saunders R, Brunel P, English S, et al. RTTOV-8-Science and validation report. Eumetsat/ ECMWF SAF Programme, Document ID NWPSAF-MOTV-007. 2005,Available from: NWP SAF Helpdesk, Met Office, FitzRoy Road, Exeter, EX1 3PB, UK.

    • 16

      Waller J A, Ballard S P, Dance S L, et al. Diagnosing horizontal and inter-channel observation error correlations for SEVIRI observations using observation-minus-background and observation- minus-analysis statistics[J]. Remote Sensing, 2016, 8(7). 851. ISSN 2072-4292

    • 17

      Joiner J, Brin E, Treadon R, et al. Effects of data selection and error specification on the assimilation of AIRS data[J].Quarterly Journal of the Royal Meteorological Society, 2007,133 (622): 181-196.

    • 18

      Pavelin E G, English S J, Eyre J R. The assimilation of cloud affected infrared satellite radiances for numerical weather prediction[J]. Quarterly Journal of the Royal Meteorological Society, 2008,134 (632):737-749.

    • 19

      LIU Hui, DONG Chao-Hua, ZHANG Wen-Jian, et al. Retrieval of clear-air atmospheric temperature profiles using AIRS observation[J].Acta Meteorological Sinica,(刘辉,董超华,张文建,等.AIRS晴空大气温度廓线反演试验.气象学报),2008,66(4):513-519.

    • 20

      Noh Y, Sohn B, Kim Y, et al. A new infrared atmospheric sounding interferometer channel selection and assessment of its impact on Met Office NWP forecasts[J].Advances in Atmospheric Sciences, 2017, 34(11):1265-1281.

    • 21

      Arai K, Liang X. Sensitivity analysis for air temperature profile estimation methods around the tropopause using simulated Aqua/AIRS data [J]. Advances in Space Research, 2009, 43(1): 845-851.

    • 22

      Tavolato C, Isaksen L. On the use of a Huber norm for observation quality control in the ECMWF 4D-Var[J].Quarterly Journal of the Royal Meteorological Society, 2015,141(690): 1514-1527.

    • 23

      YANG Yu-Han, YIN Qiu, SHU Jiong. Channel selection of atmosphere vertical sounder (GIIRS) onboard the FY-4A geostationary satellite[J].Journal of Infrared and Millimeter Waves,(杨雨晗,尹球,束炯.FY-4A大气垂直探测仪 (GIIRS) 温度探测通道优选.红外与毫米波学报), 2018,37(5):545-552.

    • 24

      BAI Wen-Guang, ZHANG Peng, ZHANG Wen-Jian, et al. An efficient method for hyper-spectral infrared atmospheric radiation transfer calculation[J].Journal of Infrared and Millimeter Waves, (白文广,张鹏,张文建,等.一种高效计算高光谱分辨率红外大气辐射传输的方法.红外与毫米波学报),2016,35(1):99-108.


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