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图1为利用FY-3E/HIRAS-II像元视场,结合同平台MERSI-LL观测辐射和ERA5再分析场资料,针对交叉定标中空间、几何和光谱匹配的不确定性分析所需的样本点对筛选过程,主要包括同平台均匀场景数据筛选和再分析场数据匹配、HIRAS-II星下点视场内匹配MERSI-LL像素,筛选得到的样本点对包含几何定位和光谱辐射信息,用于后续比对、模拟和评估。
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为了最大限度降低观测背景场不均匀引入对样本匹配不确定性分析的场景偏差,另外由于ERA5再分析场对云和降水等参数信息不能保障十分精确,且目前RTTOV在有云情况下的模拟精度不高,故实验选择在沙漠或湖泊、海洋等地表发射率较为均一的场景下挑选晴空观测背景。
晴空样本的判定条件为:根据HIRAS-II观测辐射光谱和模拟辐射光谱,选取长波红外波段窗区位置五个典型通道(810、830、850、870、890 cm−1)比较光谱亮温,要求所选通道观测辐射光谱亮温大于290 K,且与模拟辐射光谱相应通道的亮温偏差小于5 K。
另外,由于ERA5再分析场资料的时间分辨率和空间分辨率与HIRAS-II观测资料的时空网格不同,在进行辐射传输模拟之前,需要通过插值对再分析数据同HIRAS-II观测资料作时间和空间匹配。时间插值是以HIRAS-II观测资料时间为准,选择两个相邻时次的再分析资料进行线性插值;空间插值是根据HIRAS-II观测资料的地理位置信息,对再分析场进行三次样条插值。
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在筛选出一系列均匀场景晴空HIRAS-II观测资料样本后,需要对每个HIRAS-II像元瞬时视场(FOV)内匹配MERSI-LL像素,即匹配HIRAS-II FOV足迹覆盖范围内的所有MERSI-LL像元,为减少HIRAS-II观测几何方向的影响,只提取HIRAS-II具有最小扫描角度的星下点观测。HIRAS-II星下点FOV足迹视为以1°探元固定张角从卫星投影到地球表面的圆,空间分辨率为14 km,MERSI-LL星下点像元空间分辨率1 km,取HIRAS-II星下点FOV足迹内MERSI-LL观测辐射均值,与HIRAS-II观测辐射组成用于分析空间、几何和光谱匹配不确定性的标准输入样本点对数据集。
HIRAS-II星下点FOV内匹配MERSI-LL像素的主要过程包括:(1)根据HIRAS-II样本点经纬度位置确定像元中心最接近的MERSI-LL像素位置行列号,以及以行列号为中心选定40 pixel×40 pixel区域作为环境区域;(2)通过视线LOS (line-of-sight)向量[25-26]计算HIRAS-II星下点FOV足迹覆盖范围;(3)根据视场角判断并挑选HIRAS-II星下点FOV足迹范围内的所有MERSI-LL像元,并对观测辐射取均值。匹配计算过程需进行坐标系转换,涉及的坐标系包括局部球面坐标系、站心坐标系(ENU)、大地坐标系(LLA)和地心地固坐标系(ECEF),各坐标系汇总示例如图2所示。
图 2 坐标系示例。(a) ECEF坐标系(黑色),LLA坐标系(蓝色),局部ENU坐标系(红色);(b)局部ENU坐标系和局部球面坐标系(绿色)
Figure 2. Demonstration of coordinate systems. (a) ECEF (black), LLA (blue), ENU (red); (b) ENU and local spherical coordinate (green)
HIRAS-II和MERSI-LL地理信息中的经纬度表示LOS向量与地球交点位置P (见图2(a)),在大地坐标系中,大地经纬度通常代表水平位置,大地高度代表地球椭球上方的垂直位置,因此,大地坐标系可称为大地纬度(
$Lat$ )、经度($Lon$ )和高度($A$ )坐标系(LLA)。大地坐标系是大地测量中以参考椭球面为基准面建立起来的坐标系,计算中使用1984年世界大地测量系统(WGS84)作为大地测量参考。使用局部球面坐标系可以表示地球上给定点对应的卫星位置,所需要的定位信息包括卫星方位角
$S atAzi$ 、卫星天顶角$S atZen$ 以及卫星距离$Range$ (卫星与像素视场中心距离),以地球上该给定点为坐标原点(如图2(a)点P),以指向东边(E)为X轴、指向北边(N)为Y轴、垂直于该点的局部切平面指向天顶(U)为Z轴构成的三维直角坐标系称为局部东-北-天站心坐标系(ENU)。在ENU坐标系中的视线LOS向量即为卫星位置指向以观测位置坐标点P为原点的向量(见图2(b))。图2(b)中,由于局部ENU坐标系原点会随卫星观测位置不同发生变化,为在同一坐标系中表示不同卫星观测位置的LOS向量,可利用地心地固坐标系(ECEF)进行计算,简称地心坐标系(见图2(a))。地心坐标系以地球质心为坐标原点,X轴穿过本初子午线Prime Meridian (0°经度)和赤道Equator (0°纬度)的交点,Z轴与地球旋转轴重合并穿过北极,Y轴与X轴、Z轴构成右手坐标系并穿过赤道和90°经度交点。在ECEF坐标系中定义从地心(ECEF坐标系原点)指向卫星称为卫星向量
${{S A T}}$ ,定义从地心指向卫星观测地球表面交点称为卫星观测位置向量${{R}}$ ,从卫星位置指向观测地球表面交点为视线${{LOS}}$ 向量,向量构成如图3所示。则ECEF坐标系下卫星向量
${{S AT}}$ 与卫星观测位置向量${{R}}$ 和视线${{LOS}}$ 向量的关系为:$$ {{S A T = R - LOS}} $$ (1) 其中,卫星观测位置向量
${{{R}}_{{\rm{ECEF}}}}(Rx,Ry,Rz)$ 是根据经纬度和大地高度定位信息$(Lon,Lat,A)$ 由LLA坐标系转换为ECEF坐标系下得到的,由于观测位置为地球表面,大地高度$A$ 简化为0。另外,HIRAS-II和MERSI-LL同平台卫星搭载,可将卫星向量${{S A}}{{{T}}_{{\rm{ECEF}}}}$ 视为是相同的,则通过计算HIRAS-II的视线向量${{LO}}{{{{{S}}}}_{{\rm{HIRAS - II}}}}$ 和MERSI-LL的视线向量${{LO}}{{{S}}_{{\rm{MERSI - LL}}}}$ ,并且比较视线向量夹角与HIRAS-II视场半锥角的大小,以实现匹配HIRAS-II视场内的MERSI-LL像素。首先,由卫星方位角
$S atAzi$ 、卫星天顶角$S atZen$ 和卫星距离$r$ 可在局部球面坐标系$(S atAzi,S atZen,r)$ 计算视线向量,根据卫星天顶角$S atZen$ 能够近似计算卫星到像素视场中心距离$r$ :$$ r = h/\cos (S atZen) $$ (2) 式中:
$h$ 为卫星的轨道高度。经转换到局部ENU坐标系得到视线向量
${{LO}}{{{S}}_{{\rm{ENU}}}}({\rm{E,N,U}})$ ,该局部坐标系坐标原点经纬度为$(Lon,Lat)$ ;然后,通过先对ENU坐标系的东轴(E)沿顺时针方向旋转${90^ \circ } - Lat$ ,使天顶轴(U)与ECEF坐标系Z轴对齐,再对ENU坐标系的天顶轴(U)沿顺时针方向旋转${90^ \circ } + Lon$ ,使东轴(E)与ECEF坐标系X轴对齐,能够将${{LO}}{{{S}}_{{\rm{ENU}}}}({\rm{E,N,U}})$ 转换为ECEF坐标系下的视线向量${{LO}}{{{S}}_{{\rm{ECEF}}}}(LO{S_X},LO{S_Y},LO{S_Z})$ 。对于每个HIRAS-II观测FOV点经纬度
$(Lo{n_{{\rm{HIRAS - II}}}}, La{t_{{\rm{HIRAS - II}}}})$ 和几何定位信息,可以得到卫星观测位置向量${{{R}}_{{\rm{HIRAS - II}}}}$ 和视线向量${{LO}}{{{S}}_{{\rm{HIRAS - II}}}}$ ,由公式(2)计算卫星向量${{S A}}{{{T}}_{{\rm{ECEF}}}}{{ = }}{{{R}}_{{\rm{HIRAS - II}}}}{{ - LO}}{{{S}}_{{\rm{HIRAS - II}}}}$ ,再根据HIRAS-II经纬度$(Lo{n_{{\rm{HIRAS - II}}}},La{t_{{\rm{HIRAS - II}}}})$ 确定的环境区域内MERSI-LL像素的经纬度序列得到卫星观测位置向量序列${{{R}}_{{\rm{MERSI - LL}}}}$ ,则MERSI-LL的视线向量序列为${{LO}}{{{S}}_{{\rm{MERSI - LL}}}} = {{{R}}_{{\rm{MERSI - LL}}}} - {{S A}}{{{T}}_{{\rm{ECEF}}}}$ 。HIRAS-II的视线向量
${{LO}}{{{S}}_{{\rm{HIRAS - II}}}}$ 指向了FOV的视场中心,其FOV足迹是以${{LO}}{{{S}}_{{\rm{HIRAS - II}}}}$ 为轴、以探元张角$\varphi $ 一半为半锥角的锥体形成的地面投影,若MERSI-LL像素落入HIRAS-II FOV足迹范围内,则MERSI-II的视线向量${{LO}}{{{S}}_{{\rm{MERSI - LL}}}}$ 与HIRAS-II的视线向量${{LO}}{{{S}}_{{\rm{HIRAS - II}}}}$ 夹角应小于$\varphi $ 的一半,$\varphi $ 为1°。视线向量
${{LO}}{{{S}}_{{\rm{HIRAS - II}}}}$ 和${{LO}}{{{S}}_{{\rm{MERSI - LL}}}}$ 的向量夹角$\theta $ 的余弦可表示为:$$ \cos (\theta ) = \frac{{{{LO}}{{{S}}_{{\rm{HIRAS - II}}}} \cdot {{LO}}{{{S}}_{{\rm{MERSI - LL}}}}}}{{\left\| {{{LO}}{{{S}}_{{\rm{HIRAS - II}}}}} \right\|\left\| {{{LO}}{{{S}}_{{\rm{MERSI - LL}}}}} \right\|}} $$ (3) 式中:
$\left\| \cdot \right\|$ 为向量的模。公式(3)根据欧几里得向量点积公式推导得到,向量夹角$\theta $ 在$(0,\pi /2)$ 范围内,其余弦值呈递减趋势,随夹角增大而变小,所以若MERSI-LL像素落入HIRAS-II FOV足迹,则应满足:$$ \frac{{{{LO}}{{{S}}_{{\rm{HIRAS - II}}}} \cdot {{LO}}{{{S}}_{{\rm{MERSI - LL}}}}}}{{\left\| {{{LO}}{{{S}}_{{\rm{HIRAS - II}}}}} \right\|\left\| {{{LO}}{{{S}}_{{\rm{MERSI - LL}}}}} \right\|}} \gt \cos (\varphi /2) $$ (4) 式中:
$\varphi $ 为HIRAS-II探元固定张角,即视线向量${{LO}}{{{S}}_{{\rm{HIRAS - II}}}}$ 和${{LO}}{{{S}}_{{\rm{MERSI - LL}}}}$ 的向量夹角$\theta $ 小于HIRAS-II FOV半锥角,表明此时的MERSI-LL像素在HIRAS-II FOV内。 -
对HIRAS-II FOV内的MERSI-LL像素序列求辐射均值后与HIRAS-II FOV的观测辐射组成样本点对,并将HIRAS-II FOV足迹覆盖范围称为靶区,分别从空间位置、几何观测角度和光谱响应函数三个方面添加扰动,分析匹配误差引入的不确定性。
(1)空间匹配方面,以靶区辐射亮温作为标准值,通过沿经向或者纬向整体移动FOV足迹模拟空间失配,移动足迹后的靶区辐射亮温作为扰动值。比较扰动值与标准值的亮温均值偏差百分比、亮温均值偏差标准差;定义靶区亮温标准差与亮温均值之比为背景不确定度,比较FOV移动前后因空间失配造成的背景辐射亮温相对不确定度。
(2)几何匹配方面,以样本点对的HIRAS-II观测光谱辐射亮温作为标准值,将再分析数据插值到该样本点时空网格并输入至RTTOV中,通过改变卫星天顶角输出模拟光谱辐射亮温作为扰动值。比较观测几何卫星天顶角改变前后模拟光谱与标准值光谱的辐射亮温偏差和相对精度。
(3)光谱匹配方面,通过HIRAS-II红外高光谱辐射与MERSI-LL的通道光谱响应函数可模拟计算得到高光谱等效辐射,设HIRAS-II光谱辐射为
$ R(\nu ) $ ,MERSI-LL的某一通道光谱响应函数为$ S(\nu ) $ ,则模拟等效辐射$ L $ 为:$$ L = \frac{{\displaystyle\int_{{\nu _1}}^{{\nu _2}} {R(\nu )S(\nu ){\rm{d}}\nu } }}{{\displaystyle\int_{{\nu _1}}^{{\nu _2}} {S(\nu ){\rm{d}}\nu } }} $$ (5) 式中:
$ \nu $ 代表波段;$ {\nu _1} $ 和$ {\nu _2} $ 为波段的起始和终止波数。相同高光谱辐射输入条件下,由于光谱响应函数的差异将导致模拟等效辐射不同,进而影响定标精度。在不改变HIRAS-II样本光谱辐射$ R(\nu ) $ 的情况下,将$ R(\nu ) $ 与MERSI-LL的标准通道光谱响应函数$ S(\nu ) $ 计算的模拟等效辐射$ L $ 作为标准值,分别对光谱响应函数采用展宽或收缩、中心波长平移的方式进行扰动,再计算扰动后的模拟等效辐射${L'}$ 。统计所有样本点的模拟等效辐射亮温,比较扰动前后亮温均值偏差和偏差标准差,定义亮温均值偏差与标准亮温均值之比为光谱匹配误差引入的不确定度。
Uncertainty analysis of inter-calibration collocation based on FY-3E spaceborne infrared observations
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摘要: 星载红外高光谱传感器与多通道光谱传感器在轨交叉定标时能够提升数据精度和质量,交叉定标样本通常采用星下点交叉方式匹配筛选,包括空间、时间、观测几何角度和光谱匹配,匹配误差的不确定性将对最终交叉定标精度产生影响。采用FY-3E同平台红外高光谱大气探测仪HIRAS-II和中分辨率光谱成像仪MERSI-LL均匀晴空背景进行观测,根据视线向量匹配HIRAS-II星下点瞬时视场内的MERSI-LL像素,分别通过模拟视场偏移、观测天顶角偏差和光谱响应函数变化单独分析空间、观测几何角度和光谱匹配误差引入的匹配不确定度。结果表明,空间失配引起观测背景辐射亮温变化,偏移一半像元视场时的相对不确定度约为10%,达到一个像元时为25%~30%;观测几何角度失准引起光谱辐射亮温变化,观测天顶角偏移20°时的不确定度优于0.2%;光谱响应函数差异引起光谱等效辐射亮温变化,响应函数发生展宽时对吸收通道的不确定度最大约为2.5%,窗区通道为0.4%,收缩时的不确定度整体优于0.3%,平移引起的不确定度相对较小,移动5倍波长间隔时优于0.1%。Abstract:
Objective Spaceborne infrared hyperspectral sensors and multi-channel spectral sensors can continuously observe the earth for a long period of time, and have important applications in the fields of climate prediction, weather change, environmental monitoring, etc. The high-precision spectral calibration and radiation calibration of their observation data are crucial to the quantitative application of remote sensing. With the increase of operational time of satellite after being launched, the performance of the spaceborne sensors will change, which will lead to the deviation of observation data accuracy. Therefore, it is necessary to effectively improve the calibration accuracy and the data quality of the instrument through on-orbit inter-calibration. The samples of inter-calibration are generally collocated and filtered through the method of the on-orbit alternative calibration of the Global Space-based Inter-Calibration Sytem (GSICS), including spatial, temporal, observation geometry and spectral collocation through simultaneous nadir overpass (SNO) observations, and consequently achieve the goal of inter-calibration with the target sensor. The SNO observations can make two satellite sensors observe the earth from different heights at the similar time and place, which fully reduces the comparison uncertainty caused by different observation time and angle of satellites. This is a necessary prerequisite for the feasibility of inter-calibration, but these factors are also the main source of calibration uncertainty, and the uncertainty of collocating bias will have effects on the inter-calibration accuracy finally. Therefore, we analyze the uncertainty of the samples collocating processing in this paper, including spatial collocation, observation angle collocation and spectral response function collocation between sensors. Methods We establish the sifting process of inter-observation sample pairs above uniform clear-sky background scenes (Fig.1) of the infrared hyperspectral atmospheric sounder HIRAS-II and the low-light medium-resolution spectral imager MERSI-LL onboard the same platform of the FY-3E of China Fengyun-3 series sun-synchronous orbit meteorological satellite. Collocating MERSI-LL pixels within HIRAS-II nadir instantaneous field of view (IFOV) based on line-of-sight (LOS) vectors, HIRAS-II projects the FOV footprint from the satellite to the earth's surface at a fixed solid angle, and all coordinates are converted into Earth Centered Earth Fixed (ECEF) coordinate system after calculation. All MERSI-LL pixels in the coverage area of HIRAS-II FOV footprint can be determined by calculating the line-of-sight vector (Fig.3). The uncertainty of the samples collocation introduced by spatial, observation geometry and spectral collocating bias is separately analyzed by simulating IFOV shift, observation zenith angle deviation and spectral response function change, respectively. Results and Discussions The results of uncertainty analysis above each section of collocating process through cross observation of sensors on the same platform, radiation transmission model simulation and statistical analysis show that, in terms of spatial collocation, we evaluated the percentage deviation and standard deviation of radiance brightness temperature between the disturbed value and the standard value (Fig.5) by comparing the standard value of radiance brightness temperature in the target area with the disturbed value of radiance brightness temperature after simulating pixel offset, the spatial mis-collocation causes the changes of radiance brightness temperature above observed background scenes, the relative uncertainty is approximately 10% when the IFOV is shifted by half a pixel. In terms of geometric collocation, we evaluated the deviation and relative accuracy of the brightness temperature of the observed and simulated spectrum by comparing the brightness temperature sample of spectrum observed by HIRAS-II with the simulated spectral brightness temperature after changing the satellite zenith angle, it is found that the misalignment of observation geometry causes deviation of spectrum radiance brightness temperature, the uncertainty is less than 0.2% when the observed zenith angle is shifted by 20 degree (Fig.7). In terms of spectral collocation, the hyperspectral equivalent radiance can be obtained by simulating and calculating the HIRAS-II infrared hyperspectral radiance and channel spectral response function of MERSI-LL. The difference of the spectral response function causes bias of spectral equivalent radiance brightness temperature, the uncertainty of the absorption channel and window channle is approximately 2.5% and 0.4% respectively for expanding the response function, and the uncertainty is better than 0.3% overall for shrinking the response function, the uncertainty is relatively small for shifting response function, and it is better than 0.1% when shifting five times the wavelength interval (Fig.9). Conclusions In this study, we analyzed the uncertainty and its influence introduced by observation collocation in terms of spatial, observation geometry and spectral collocation, which are aimed at the spaceborne infrared hyperspectral sensors and multi-channel spectral sensors before inter-calibration. We used the pixel matching method above observation field based on the line-of-sight vector to separately analyze the uncertainty introduced by spatial, observation geometry and spectral collocating bias. The spatial mis-collocation caused by IFOV shift leads to the change of observation background radiance, the relative uncertainty is approximately 25%-30% when the IFOV is shifted by a pixel. In order to reduce the uncertainty introduced by pixel offset, the offset distance should be limited to half of the spatial resolution of the nadir instantaneous field of view. The misalignment of observation geometry caused by observation zenith angle difference leads to the bias of observation background radiance, and the bias is more obvious in vapor channel, the deviation of observation zenith angle should be constrained within 10 degree or more less. The deviation of hyperspectral equivalent radiance caused by the difference of spectral response function has an impact on the calibration accuracy, the effective bandwidth change of spectral response function will cause greater uncertainty relative to the central wavelength shift of spectral response function. This study provides a reference for setting reasonable threshold in the condition of sifting collocated samples before inter-calibration, and also provides support for improving accuracy of inter-comparison and calibration. -
Key words:
- infrared inter-calibration /
- inter-collocation /
- uncertainty
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图 5 MERSI-LL 3.8 μm通道背景模拟HIRAS-II星下点FOV沿经向偏移。(a)靶区辐射亮温;(b)与标准靶区亮温的绝对偏差百分比;(c)与标准靶区亮温的偏差标准差;(d)靶区亮温标准差与均值之比
Figure 5. Shift along longitude of HIRAS-II FOV within band 3.8 μm of MERSI-LL. (a) Randiance brightness temperature of target; (b) Absolute bias percent of brightness temperature vs standard target; (c) Standard bias of brightness temperature vs standard target; (d) Ratio of standard bias and mean bias of standard target
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