基于Sentinel-2A数据的不同生育期枣树叶片SPAD值估算

王仁军, 郑江华, 卢宾宾, 尼格拉·吐尔逊, 李曦光, 罗磊

王仁军, 郑江华, 卢宾宾, 尼格拉·吐尔逊, 李曦光, 罗磊. 基于Sentinel-2A数据的不同生育期枣树叶片SPAD值估算[J]. 武汉大学学报 ( 信息科学版). DOI: 10.13203/j.whugis20230065
引用本文: 王仁军, 郑江华, 卢宾宾, 尼格拉·吐尔逊, 李曦光, 罗磊. 基于Sentinel-2A数据的不同生育期枣树叶片SPAD值估算[J]. 武汉大学学报 ( 信息科学版). DOI: 10.13203/j.whugis20230065
WANG Renjun, ZHENG Jianghua, LU Binbin, TUERXUN Nigela, LI Xiguang, LUO Lei. Estimating of SPAD value for jujube leaves at different growth stages using the Sentinel-2A image[J]. Geomatics and Information Science of Wuhan University. DOI: 10.13203/j.whugis20230065
Citation: WANG Renjun, ZHENG Jianghua, LU Binbin, TUERXUN Nigela, LI Xiguang, LUO Lei. Estimating of SPAD value for jujube leaves at different growth stages using the Sentinel-2A image[J]. Geomatics and Information Science of Wuhan University. DOI: 10.13203/j.whugis20230065

基于Sentinel-2A数据的不同生育期枣树叶片SPAD值估算

基金项目: 

新疆特色林果业典型树种-红枣分布遥感监测与种植面积估算(202105140018);新疆特色林果业典型树种-红枣种植面积与主要健康参数遥感反演(202067007); 新疆天山雪松项目(2020XS04)。

详细信息
    作者简介:

    王仁军,硕士研究生,主要从事农业遥感研究。renjun20221@163.com

    通讯作者:

    郑江华,博士,教授。zheng.jianghua@xju.edu.cn

  • 中图分类号: TP79

Estimating of SPAD value for jujube leaves at different growth stages using the Sentinel-2A image

  • 摘要: 准确估算枣树叶片叶绿素含量不仅能反映其长势及营养状况,而且还能为田间管理提供科学依据。该研究以枣树展叶期、坐果期及成熟期叶片为研究对象,旨在评估Sentinel-2A数据估算枣树叶片相对叶绿素含量(SPAD值)的潜力。基于5种典型植被指数框架,利用Sentinel-2A数据的10个波段两两组合构建光谱指数,将构建的光谱指数与实测SPAD值进行相关性分析,通过相关系数筛选最优光谱指数。基于最优光谱指数,分别采用多元线性逐步回归模型(MLSR)、支持向量机回归模型(SVR)和随机森林回归模型(RFR)建立SPAD值估算模型,以决定系数(R2)和均方根误差(RMSE)作为模型评价指标,通过模型评估筛选出估算枣树叶片SPAD值的最优模型。结果表明:(1)3个生育期优选的5种最适光谱指数主要由红波段、红边波段和近红外波段组成,且成熟期优选的5种光谱指数与SPAD值相关性最高,均通过0.01的显著性水平检验,相关系数的绝对值均大于0.37;(2)3个生育期建立的估算模型精度有所差异,其中坐果期估算精度最差,展叶期和成熟期估算精度因模型而异,基于MLSR和SVR模型,成熟期的估算精度最高,基于RFR模型,展叶期精度最高,且展叶期的RFR模型为所有估算模型中的最佳模型,R2和RMSE分别为0.90和1.04;(3)采用的MLSR、SVR和RFR三种回归模型中,MLSR和SVR估算结果较为相似,RFR为最优估算模型,且最优估算模型在不同的植被覆盖场景下具有较强的普适性。以上研究结果表明,Sentinel-2A数据适用于估算枣树叶片SAPD值,且展叶期的RFR模型可作为枣树叶片SPAD值估算的最优模型,研究结果可为基于Sentinel-2A数据估算枣树SPAD值的研究提供重要参考。
    Abstract: Objectives: The accurate estimation of leaf chlorophyll content of jujube can not only reflect its growth and nutritional status, but also provide scientific basis for field management. The aim of this study was to evaluate the potential of Sentinel-2A data for estimating soil plant analysis development (SPAD) values of jujube leaves during leaf spreading, fruit setting stage and fruit ripening stage. Methods: In this paper, five traditional vegetation indices related to chlorophyll content were selected, and based on the framework of five traditional vegetation indices, ten bands of Sentinel-2A data were used to improve the traditional vegetation indices, and five spectral indices were constructed for three growth periods respectively. The correlation between the constructed spectral index and the measured SPAD value was analyzed, and the optimal spectral index was screened by the correlation coefficient. Based on the optimal spectral index, multiple linear stepped-regression model (MLSR), support vector machine regression model (SVR) and random forest regression model (RFR) were used to establish SPAD estimation models. The coefficient of determination (R2) and Root mean square error (RMSE) were used as model evaluation indexes, and the optimal model for estimating the SPAD value of jujube leaves was screened out through model evaluation. Results: The results showed that:the five optimal spectral indices optimized at three growth stages were mainly composed of red band, red-edge band and near-infrared band, and the five optimal spectral indices at fruit ripening stage had the highest correlation with SPAD value, all of which passed the significance level test of 0.01, and the absolute values of correlation coefficients were all greater than 0.37. The accuracy of estimation models established at different growth stages was different, and the accuracy of estimation at fruit setting stage was the worst. The estimation accuracy of leaf spreading stage and fruit ripening stage varied according to the models. The accuracy of fruit ripening stage was the highest based on MLSR and SVR, while the accuracy of leaf spreading stage was the highest based on RFR. The RFR model of leaf spreading stage was the best model among all the estimation models, R2 and RMSE were 0.90 and 1.04, respectively. Among the three regression models used, MLSR, SVR and RFR, the estimation results of MLSR and SVR are similar, and RFR is the best estimation model, and the best estimation model has strong universality under different vegetation cover scenarios. Conclusions: The above results show that Sentinel-2A data is suitable for SAPD estimation of jujube leaves, and the RFR model at leaf spreading stage can be used as the optimal model for SPAD estimation of jujube leaves. The results can provide an important reference for the study of estimating SPAD value of jujube based on Sentinel-2A data.
  • 精密单点定位(precise point positioning, PPP)技术具有定位精度高,数据采集方便,数据处理简单等优点,成为近年来实时精密定位服务的重要手段。实时精密单点定位服务将卫星精密轨道和钟差实时播发给用户[1]。IGS已经开展了实时实验计划(real-time pilot project, RTPP),各个分析中心播发的GPS实时精密轨道精度为4~8 cm,精密钟差精度为0.2~0.8 ns。实时精密轨道通常采用的是超快速预报轨道,由于超快速轨道精度不如最终精密轨道,为了实现高精度实时定位,通过实时估计卫星钟差吸收部分轨道误差。国内外学者对实时精密卫星钟差估计算法进行了大量研究,主要包括非差模式和历元间差分模式。非差模式精密卫星钟差估计方法待估参数过多,计算效率较低[2]。采用历元间差分方法时,模糊度参数被消除,计算速率加快,但初始时刻卫星钟差会引入与卫星相关的偏差[3]。为了消除该项偏差的影响,Zhang等[4]提出了利用非差相位和伪距观测值和历元间差分相位和伪距观测值并行计算的方法。Ge等[5]提出了利用历元间差分相位观测值和非差伪距观测值并行计算的方法。

    全球卫星导航系统发展迅猛,继美国的GPS、俄罗斯的GLONASS后,欧洲正在开发Galileo卫星导航系统,我国已经建立了功能完善的第二代北斗区域卫星导航系统(Beidou Navigation Satellite System, BDS)[6]。相关研究表明多系统融合增加了可观测卫星数目,改善了卫星空间几何结构,提高了定位的准确性,可靠性和连续性[7]。因此,多系统融合逐渐成为了高精度卫星导航定位广大用户的必然选择,而多系统实时卫星钟差的精确估计是实现多系统高精度实时定位服务的前提。本文对基于历元间差分相位观测值和非差伪距观测值的卫星钟差估计方法进行了改进,实现了GPS、GLONASS、Galileo和BDS多系统卫星钟差联合快速估计。

    基于无电离层组合伪距和相位的观测方程为:

    $$ \left\{ \begin{array}{l} P_r^s = \rho _0^s + c\left( {d{t_r}-d{t^s}} \right) + {T_r} + c\left( {{B_r}-{B^s}} \right) + {e_s}\\ L_r^s = \rho _0^s + c\left( {d{t_r}-d{t^s}} \right) - \lambda {N^s} + \\ \;\;\;\;\;\;\;{T_r} + c\left( {{b_r} - {b^s}} \right) + \varepsilon_s \end{array} \right. $$ (1)

    式中,r为测站号;s为卫星号;PrsLrs为无电离层组合伪距和相位观测值;ρ0s为站-星间几何距离;c为光速;dtr为接收机钟差;dts为卫星钟差;Tr为传播路径上对流层延迟误差;Ns为无电离层组合整周模糊度;λ为无电离层组合波长;Brbr分别为接收机端无电离层组合伪距和相位的硬件延迟;Bsbs分别为卫星端无电离层组合伪距和相位的硬件延迟;esεs分别为伪距和相位的测量噪声,多路径误差通常归入到测量噪声内。

    参数估计时,接收机伪距硬件延迟Br被接收机钟差dtr吸收,卫星伪距硬件延迟Bs被卫星钟差dts吸收,固定测站坐标,式(1)线性化为:

    $$ \left\{ \begin{array}{l} {v_{P_r^s}} = c\left( {\delta {t_r}-\delta {t^s}} \right) + m_r^sd{T_r}-{\rm{OM}}{{\rm{C}}_{P_r^s}}\\ {v_{L_r^s}} = c\left( {\delta {t_r}-\delta {t^s}} \right) - \lambda {{\tilde N}^s} + m_r^sd{T_r} - {\rm{OM}}{{\rm{C}}_{L_r^s}} \end{array} \right. $$ (2)

    式中,δtr=dtr+Brδts=dts+Bs;$ {{\tilde N}^s}$=Ns+c(br-bs-Br+Bs)/λ;OMCPrs=Prs-ρ0s;OMCLrs=Lrs-ρ0smrsdTr分别为对流层湿延迟投影函数和残余误差;vPrsvLrs分别为伪距和相位观测值残差。

    由式(2)可得历元间差分的相位观测值为:

    $$ \Delta {v_{L_r^s}} = c\left( {\Delta \delta {t_{r, {\rm{sys}}}}-\Delta \delta {t^s}} \right) + \Delta m_r^sd{T_r}-\Delta \;\;{\rm{OM}}{{\rm{C}}_{L_r^s}} $$ (3)

    式中,sys=G、R、E、B,文中G代表GPS,R代表GLONASS,E代表Galileo,B代表BDS;Δδtr, sys为系统sys相邻历元间接收机钟差改正数之差;Δδts为相邻历元间卫星钟差改正数之差;在规定的弧段内,对流层湿延迟的投影函数mrs发生变化,对投影函数进行历元间做差分得Δmrs;天顶对流层湿延迟残余误差参数dTr作为分段线性常数估计;ΔOMCLrs为相位观测值与计算值之差OMCLrs的历元间差,ΔvLrs为相邻历元间相位观测值残差之差。

    多系统卫星钟差估计时,同一测站不同系统接收机端伪距硬件延迟不同,不同系统接收机钟差存在差异[8]。此时可以估计一个接收机钟差和多个系统时间差,或者同时估计若干个接收机钟差[9]。本文同时估计了4个系统的接收机钟差参数。则多模融合卫星钟差估计误差为:

    $$ \left\{ \begin{array}{l} \Delta {v_{L_r^i}} = c\left( {\Delta \delta {t_{r, G}}-\Delta \delta {t^i}} \right) + \Delta m_r^id{T_r}-\Delta \;{\rm{OM}}{{\rm{C}}_{L_r^i}}\\ \Delta {v_{L_r^j}} = c\left( {\Delta \delta {t_{r, R}}-\Delta \delta {t^j}} \right) + \Delta m_r^jd{T_r} - \Delta \;{\rm{OM}}{{\rm{C}}_{L_r^j}}\\ \Delta {v_{L_r^k}} = c\left( {\Delta \delta {t_{r, E}} - \Delta \delta {t^k}} \right) + \Delta m_r^kd{T_r} - \Delta \;{\rm{OM}}{{\rm{C}}_{L_r^k}}\\ \Delta {v_{L_r^l}} = c\left( {\Delta \delta {t_{r, B}} - \Delta \delta {t^l}} \right) + \Delta m_r^ld{T_r} - \Delta \;{\rm{OM}}{{\rm{C}}_{L_r^l}} \end{array} \right. $$ (4)

    式中,i=1, …, nGj=1, …, nRk=1, …, nEl=1, …, nBnsys为测站r接收到系统sys卫星个数;δtr, Gδtr, R、Δδtr, E、Δδtr, B分别为测站相邻历元间的GPS、GLONASS、Galileo和BDS接收机钟差改正数之差;Δδti、Δδtj、Δδtk、Δδtl分别为第i颗GPS卫星,第j颗GLONASS卫星,第k颗Galileo卫星,第l颗BDS卫星的相邻历元间卫星钟差改正数之差;Δmri、Δmrj、Δmrk、Δmrl分别为第i颗GPS卫星,第j颗GLONASS卫星,第k颗Galileo卫星,第l颗BDS卫星对应的对流层湿延迟投影函数之差;ΔOMCLri、ΔOMCLrj、ΔOMCLrk、ΔOMCLrl分别为第i颗GPS卫星,第j颗GLONASS卫星,第k颗Galileo卫星,第l颗BDS卫星的相位观测值与计算值之差的历元间差;ΔvLri、ΔvLrj、ΔvLrk、ΔvLrl分别第i颗GPS卫星,第j颗GLONASS卫星,第k颗Galileo卫星,第l颗BDS卫星的相邻历元间相位观测值残差之差。

    对式(4)采用均方根信息滤波方法进行参数估计。需要指出的是接收机钟差是相对量,对同一系统的所有跟踪站的接收机钟差采用重心基准$ \sum\limits_{r = 1}^{{m_{sys}}} {\Delta \delta {t_{r, {\rm{sys}}}}} = 0$进行约束,msys为跟踪站到系统sys卫星的测站个数。

    由式(4)可以得到历元k时刻卫星s的历元间差分钟差改正数Δδts(k),则历元k时刻卫星s的钟差改正数为:

    $$ \delta {t^s}\left( k \right) = \delta {t^s}\left( {{i_0}} \right) + \sum\limits_{i = {i_0} + 1}^k {\Delta \delta {t^s}\left( i \right)} $$ (5)

    式中,i0为卫星s初始历元;δts(i0)为初始历元i0对应的卫星钟差改正数;Δδts(i)为历元i对应的卫星钟差改正数历元间差。

    由式(2)可得历元k时刻的非差伪距观测值误差方程为:

    $$ \begin{array}{l} {v_{P_r^s(k)}} = c\left( {\delta {t_r}\left( k \right)-\delta {t^s}\left( k \right)} \right) + \\ \;\;\;\;\;\;\;m_r^s\left( k \right)d{T_r}-{\rm{OM}}{{\rm{C}}_{P_r^s\left( k \right)}} \end{array} $$ (6)

    由历元间差分相位观测值可以得到的非常精确的对流层延迟误差和历元间差分卫星钟差[4-5]。将式(3)求得的dTr和式(5)带入式(6),可得:

    $$ {v_{P_r^s\left( k \right)}} = c\left( {\delta {t_r}\left( k \right)-\delta {t^s}\left( {{i_0}} \right)} \right)-{\rm{om}}{{\rm{c}}_{P_r^s\left( k \right)}} $$ (7)

    式中

    $$ {\rm{om}}{{\rm{c}}_{P_r^s\left( k \right)}} = c\sum\limits_{i = {i_0} + 1}^k {\Delta \delta {t^s}\left( i \right)}-m_r^s\left( k \right)d{T_r} + {\rm{OM}}{{\rm{C}}_{P_r^s\left( k \right)}} $$

    历元间差分方法同时对相位与伪距观测值进行了差分,由式(5)可以看出,求得的卫星钟差受到δts(i0)的影响,当采用导航星历进行计算时,会导致数十纳秒的偏差[2, 4-5]

    式(7)可看做利用精确求得的卫星钟变化来平滑伪距残差,因此δts(i0)经过一段时间才会收敛,才能被用于卫星钟差的计算,经测试,收敛时间大概需要20分钟。

    本文在文献[5]的基础上,利用式(7),对同一系统同一测站观测到的卫星st进行星间做差,消除接收机钟差可得:

    $$ {v_{P_r^{st}\left( k \right)}} = c\left( {\delta {t^t}\left( {{i_0}} \right)-\delta {t^s}\left( {{i_0}} \right)} \right)-{\rm{om}}{{\rm{c}}_{P_r^{st}\left( k \right)}} $$ (8)

    式中,δtt(i0)和δts(i0)分别为卫星ts在历元i0对应的卫星钟差改正数;omcPrst(k)=omcPrt(k)-omcPrs(k)vPrst(k)为卫星ts在历元k对应的伪距观测值残差星间差。

    式(8)与测站无关,采用最小二乘估计即可得到相应卫星的初始时刻钟差改正数δts(i0)。需要指出的是卫星钟差是相对量,采用重心基准$\sum\limits_{s = 1}^n {\delta {t^s}} \left( {{i_0}} \right) = 0 $进行约束,n为历元i0时刻观测到的同一系统卫星个数。

    求出卫星s初始时刻i0的卫星钟差改正数δts(i0)后,历元k时刻卫星s的钟差可以表示为:

    $$ {t^s}\left( k \right) = {t^s}{\left( k \right)_0} + \delta {t^s}\left( {{i_0}} \right) + \sum\limits_{i = {i_0} + 1}^k {\mathit{\Delta }\delta {\mathit{t}^s}\left( i \right)} $$ (9)

    式中,ts(k)0为历元k时刻由导航星历得到的卫星钟差初值;ts(k)为历元k时刻卫星s的钟差。

    为了对本文算法的精度进行分析,采用2014年9月17日(年积日为260天)的全球分布的50个实测跟踪站数据,基于均方根信息滤波单历元解算多系统卫星钟差,测站分布如图 1所示。由于GNSS (Global Navigation Satellite System)观测值是测站与卫星间的相对时间延迟,所以本文所求的卫星钟差是相对于某基准钟的相对钟差。研究表明,基准钟的精度优于10-6 s,相对钟差和绝对钟差对定位的影响是等价的[2]。本文为了保证基准钟的钟差精度及实时估计卫星钟差的需要,以所有跟踪站同一系统的接收机钟差的重心基准作为基准钟,本文所求的同一系统的卫星钟差是相对于该基准钟的相对钟差。

    图  1  GNSS测站分布(地图上中国国界依据中国地图(中国地图出版社出版1:60万,ISBN9787503154032,审图号GS(2009)299)
    Figure  1.  Distribution of GNSS Tracking Stations

    本文对估计的多系统卫星钟差的精度评价采用与武汉大学多系统最终精密卫星钟差做二次差的方法。首先,选取同一系统内某一卫星作为参考星,参考星要尽量选择历元数最多的卫星,做差时GPS、GLONASS、Galileo和BDS选择的参考星依次为G09、R05、E11和C01。为了消除卫星钟差估计时基准钟选择的不同产生的影响,将本文估计的卫星钟差与武汉大学卫星钟差中的相应卫星与参考星的钟差做一次差。然后将计算结果与武汉大学的结果做二次差,这样做可以有效地反映出本文估计的卫星钟差与武汉大学最终精密卫星钟差之间的符合程度[2, 4-5]图 2~图 4分别为GPS、GLONASS、BDS和Galileo系统卫星钟差与武汉大学最终精密卫星钟差二次差的均方根(root mean square,RMS)。从中可以看出,采用本文算法求得的GPS,GLONASS,Galileo和BDS卫星钟差与武汉大学最终精密卫星钟差二次差的均方根都优于0.2 ns,其中GPS所有卫星钟差二次差均方根的平均值为0.145 ns,GLONASS所有卫星钟差二次差均方根的平均值为0.188 ns,BDS和Galileo卫星钟差二次差均方根的平均值为0.139 ns。

    图  2  GPS卫星钟差精度
    Figure  2.  Accuracy of GPS Satellites Clock Offsets
    图  3  GLONASS卫星钟差精度
    Figure  3.  Accuracy of GLONASS Satelllites Clock Offsets
    图  4  BDS和Galileo卫星钟差精度
    Figure  4.  Accuracy of BDS and Galileo Satelllites Clock Offsets

    为了验证算法的正确性,将估计的多模卫星钟差应用于PPP动态定位,并与武汉大学最终精密卫星钟差的定位结果比较。为了排除轨道因素的影响,不同卫星钟差定位解算时,卫星轨道都固定为武汉大学最终精密卫星轨道。选取了多模跟踪站九峰站进行定位试验,本文估计卫星钟差时未使用该站数据,采用GPS、GPS/GLONASS、GPS/BDS、GPS/GLONASS/BDS和GPS/GLONASS/BDS/Galileo 5种不同的动态定位模式,统计了东、北和高三个分量偏差的均方根,从第3小时开始进行精度统计以保证三个方向上偏差小于10 cm。

    图 5图 6分别为采用武汉大学最终精密钟差和本文估计的精密钟差的定位结果。从中可以看出,对于九峰站,本文估计的GPS卫星钟差的定位结果优于武汉大学卫星钟差的定位结果,这主要是因为实验所用的跟踪站在中国境内比较集中,估计的卫星钟差更适用于该区域内测站。无论是对于本文估计的卫星钟差还是武汉大学的卫星钟差,多系统融合定位精度都得到了极大提高,GPS/BDS、GPS/GLONASS/BDS融合定位平面精度优于1 cm,高程方向优于3 cm,由于Galileo卫星数较少,GPS/GLONASS/BDS/Galileo四系统融合定位相对于GPS/GLONASS/BDS融合定位没有明显提高。另外,除了GPS,基于本文估计的卫星钟差的其余四种定位模式的定位结果与基于武汉大学的卫星钟差的定位结果差距在1 cm左右,这一方面可能是由于历元间差分观测值测量噪声变大,估计的卫星钟差精度比基于非差模式的钟差略差,另一方面可能是由于武汉大学估计多系统卫星轨道和钟差时用到九峰站的数据,该站定位结果与武汉大学最终精密卫星钟差内符合性较好。

    图  5  基于武汉大学最终精密钟差的九峰站动态精密单点定位结果
    Figure  5.  Multi-GNSS PPP Results with Satellites Clock Offsets Generated by Wuhan University
    图  6  基于本文估计的精密钟差的九峰站动态精密单点定位结果
    Figure  6.  Multi-GNSS PPP Results with Satellites Clock Offsets Estimated in this Article

    本文多模卫星钟差估计分为两步。首先,采用历元间差分相位观测值求解精确的卫星钟差变化和对流层湿延迟改正;然后,采用非差伪距观测值求解初始时刻卫星钟差改正数。本文不需要采用并行计算的方法,待初始时刻卫星钟差改正数收敛以后即可获得高精度的多模卫星钟差。由于相位观测值历元间差分消除了模糊度参数,而伪距观测值星间差分消除了接收机钟差参数,在保证了卫星钟差精度的基础上,提高了计算效率,该算法非常适合应用于多系统实时卫星钟差估计。

    基于本文算法得到的多模精密卫星钟差与武汉大学最终精密卫星钟差互差优于0.2 ns。精密单点定位结果显示与利用武汉大学最终精密产品的定位结果精度相当,说明基于该算法得到的多模精密卫星钟差完全可以满足高精度导航定位用户的需要。

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