海洋生态系统动力学模型中控制参数时空分布的反演研究
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摘要
研究海洋生态学的目的是，通过加强对全球海洋生态系统结构和功能的认识，来提高预测生态系统响应全球变化的能力。发展生态系统动力学模型成为对复杂的海洋环境进行研究的一种重要手段。模型中参数的取值很大程度上影响着模拟效果。在以往海洋生态模拟工作中，部分研究者在一定程度上优化出随空间变化的生态参数，也有研究表明关键生态参数在时间上存在变化，但是至今没有研究考虑同时随时间和空间变化的参数。本文在改进参数优化方案的基础上，利用伴随同化方法优化出随时空变化的参数，提高了模拟精度。
在SODA数据提供的背景场下，本文将伴随同化方法应用于一个全球尺度的三维海洋生态系统动力学模型，该模型含有NPZD（营养盐、浮游植物、浮游动物、碎屑）四个状态变量。
基于参数空间分布，在理想实验中同化由模型产生的表层浮游植物“观测”数据，单独反演空间变化的浮游植物最大生长率Vm，其它参数取常数并保持不变。通过改进步长因子，得到最优的参数调整方案，同化效率明显提高：与前人的方案相比，在同化相同步数的情况下，约化后的代价函数值（RCF）、模拟与“观测”的平均误差（MAE）以及反演参数与给定参数的之间的相对误差（RE）均明显减小，反演的空间变化曲面与给定的空间变化曲面基本一致。通过探讨不同独立点方案和影响半径的选择对模拟结果的影响，找出独立点间的距离与最优影响半径之间的比例关系，为接下来的实验提供有利参考。通过比较不同时间步长对实验结果的影响，发现减小时间步长，计算量大大增加，但是对模拟结果影响不大。同时反演五个给定空间变化的参数，即影响生态机制的关键参数Vm、Gm、Dp、Dz、e（统称为KP），模拟精度和同化效率得到提高，各参数的RE都在6%以内，表明在海洋生态系统动力学伴随同化模型中通过优化步长因子，选择适当的独立点方案和时间步长，能够提高同化效率和模拟精度。通过对所有理想实验的结果进行线性回归分析，发现反演前后参数的RE与表层浮游植物的MAE正相关，两者的相关系数为0.8，说明表层浮游植物的MAE不仅能反应模拟结果误差的大小，在一定程度上还能反映参数反演结果的优劣，因此浮游植物的MAE可以在实际实验中作为检验参数优化正确与否的指标。
在上述工作的基础上，进行实际实验。将一年分为72个过程（每个过程5天），划定16°N-44°N，173°E-142°W（位于北太平洋）以及16°N-44°N，167°W-122°W（位于南太平洋）作为重点关注区域。针对每一个区域，通过同化每一个过程的SeaWiFS表层叶绿素数据，优化5个KP，得到了它们在该区域的时空分布。对于每一个KP，首先，分别将其在时间和空间上求平均，得到参数的空间分布场（KPS）和时间分布序列（KPT）；其次，将KPS在空间上求平均（或者将KPT在时间上求平均），得到一个常数（KPC）；最后，利用KPS、KPT和KPC表示出KP的另一种时空变化形式KPST，它减少了模拟过程中变量个数。分析结果表明，无论是空间分布还是时间分布，Vm、Dz和e均具有相同的变化趋势，相关系数可达0.99，Dp和Gm亦然；而Vm、Dz和e的变化趋势与Dp和Gm的变化趋势呈负相关，相关系数可达-0.99。将区域A与区域A’内统计得到的KPT的距平进行对比，结果表明，对于每一个参数而言，其距平随时间和空间变化，Vm、Dz和e的距平在冬半年为正值，在夏半年为负值，而Dp和Gm的距平在冬半年为负值，在夏半年为正值。5个参数的变化趋势符合物理意义和生态机制。
将模型中的参数分别按上述4种形式赋值，运行正向模式，模拟时间为1年。实验结果表明考虑参数时空分布的实验误差最小。说明在海洋生态系统动力学数值模拟中，与只考虑参数的空间分布、只考虑参数的时间分布以及把参数看作不随时空变化的常数相比，考虑参数时空分布更合理，有利于提高模拟精度；伴随同化技术在优化时空变化的参数方面，是一种有效的，值得推广的方法，它为我们研究生态系统的变化机制、对生态系统进行模拟和预报提供科学的决策依据。
Advancing our understanding of the structure and functioning of the global oceanecosystem, its major subsystems, and its response to physical forcing is the scientificresearcher's common goal, so that a capability can be developed to forecast theresponses of the marine ecosystem to global change. Developing the ecosystemdynamics model is becoming an important tool for studying the complicated marineenvironment. In most previous studies, the temporal and spatial variation of primaryproductivity and the concentration of ecological variables have been studied. Someresearches realize the spatial variations of the parameters, but the temporal variationsof key parameters are always ignored or not taken into account at all. In this study, thespatial and temporal variations of the parameters are realized, which improves thesimulation precision.
In this effort, the adjoint variational method is applied to a3D marine ecosystemmodel (NPZD-type) and its adjoint model, which are built on global scale based onclimatological environment provided by SODA. The numerical study and assimilationexperiments are implemented within a depth of200m.
In twin experiments, model-generated data of phytoplankton in the surface layerare served as fictitious observations. When the spatially varying Vm (maximumuptake rate of nutrient by phytoplankton) is estimated alone, new strategies aredesigned to optimize the step-length which is used to adjust the parameters preferablyand the assimilation efficiency is improved. On the condition that the same step isemployed, the reduced cost function (RCF), the mean absolute error of phytoplanktonin the surface layer (MAE) and the relative error (RE) of Vm between given andsimulated values decrease obviously compared with strategy in previous work. Based on the strategy above, how would the distribution schemes of spatial parameterizationand influence radius affect the results is discussed. The simulation precision is thehighest when the rate of dependent grid distance to influence radius is1.6, whichprovides for future experiments. The influence of time step was studied then and it isfound that the assimilation recovery would not be more successful with a smaller timestep of3hours compared with6hours. So6hours is the better option, by which thecomputational efficiency is improved. On the basis of the above work, when the fivekey parameters (KP) were estimated simultaneously, the given spatial variations couldbe reproduced, and the REs are less than6%. Analysis of the results of twinexperiments by linear regression method demonstrates that the relationship betweenRE of parameters and MAE is direct ratio with a correlation coefficient of0.8, soMAE can be considered as a criterion to evaluate both simulation results andparameter estimation which is useful in practical application.
Real experiments are conducted based on the conclusions above.16°N-44°N,173°E-142°W and16°N-44°N,167°W-122°W are selected as study area. One year isdivided into72periods, each of which is five days long. Spatio-temporal variation ofKP was optimized by assimilating phytoplankton data in the surface layer in eachstudy area. For each study area, the RCF and MAE in each assimilation perioddecrease obviously after assimilation. The spatially varying KP (KPS), temporallyvarying KP (KPT) and constant KP (KPC) are obtained by averaging KP of spatialand temporal variation respectively. Another type of spatio-temporal KP (KPST) isrepresented by KPS, KPT and KPC. After the correlation analysis of KP, either KPS orKPT, it is found that there is the same distribution characteristics and variation trendbetween Vm, Dz and e. The correlation coefficient can reach0.99, and the relationbetween Dp and Gm is versa. After the comparison of KPT in the two study area, it isfound that KPT anomaly is time-varying. The anomaly of Vm, Dz and e are positivevalue in winter half year and negative value in summer half year, and the anomaly ofDp and Gm is versa, which accords with the real ecological mechanism.
The model is run with KPS, KPT, KPC, and KPST respectively, and it is found that MAE is the minimum when KP are spatio-temporal variation (KPST), whileMAE reaches its maximum when KP are constant (KPC). KPST, representation ofspatio-temporal variation, reduces the variable number in model calculation.Therefore the spatio-temporal variation of parameters, which is the focus of severalresearchers, is reasonable and necessary and the adjoint variational method is a usefultool for optimizing the spatio-temporal parameters in a dynamical marine ecosystemmodel.
在SODA数据提供的背景场下，本文将伴随同化方法应用于一个全球尺度的三维海洋生态系统动力学模型，该模型含有NPZD（营养盐、浮游植物、浮游动物、碎屑）四个状态变量。
基于参数空间分布，在理想实验中同化由模型产生的表层浮游植物“观测”数据，单独反演空间变化的浮游植物最大生长率Vm，其它参数取常数并保持不变。通过改进步长因子，得到最优的参数调整方案，同化效率明显提高：与前人的方案相比，在同化相同步数的情况下，约化后的代价函数值（RCF）、模拟与“观测”的平均误差（MAE）以及反演参数与给定参数的之间的相对误差（RE）均明显减小，反演的空间变化曲面与给定的空间变化曲面基本一致。通过探讨不同独立点方案和影响半径的选择对模拟结果的影响，找出独立点间的距离与最优影响半径之间的比例关系，为接下来的实验提供有利参考。通过比较不同时间步长对实验结果的影响，发现减小时间步长，计算量大大增加，但是对模拟结果影响不大。同时反演五个给定空间变化的参数，即影响生态机制的关键参数Vm、Gm、Dp、Dz、e（统称为KP），模拟精度和同化效率得到提高，各参数的RE都在6%以内，表明在海洋生态系统动力学伴随同化模型中通过优化步长因子，选择适当的独立点方案和时间步长，能够提高同化效率和模拟精度。通过对所有理想实验的结果进行线性回归分析，发现反演前后参数的RE与表层浮游植物的MAE正相关，两者的相关系数为0.8，说明表层浮游植物的MAE不仅能反应模拟结果误差的大小，在一定程度上还能反映参数反演结果的优劣，因此浮游植物的MAE可以在实际实验中作为检验参数优化正确与否的指标。
在上述工作的基础上，进行实际实验。将一年分为72个过程（每个过程5天），划定16°N-44°N，173°E-142°W（位于北太平洋）以及16°N-44°N，167°W-122°W（位于南太平洋）作为重点关注区域。针对每一个区域，通过同化每一个过程的SeaWiFS表层叶绿素数据，优化5个KP，得到了它们在该区域的时空分布。对于每一个KP，首先，分别将其在时间和空间上求平均，得到参数的空间分布场（KPS）和时间分布序列（KPT）；其次，将KPS在空间上求平均（或者将KPT在时间上求平均），得到一个常数（KPC）；最后，利用KPS、KPT和KPC表示出KP的另一种时空变化形式KPST，它减少了模拟过程中变量个数。分析结果表明，无论是空间分布还是时间分布，Vm、Dz和e均具有相同的变化趋势，相关系数可达0.99，Dp和Gm亦然；而Vm、Dz和e的变化趋势与Dp和Gm的变化趋势呈负相关，相关系数可达-0.99。将区域A与区域A’内统计得到的KPT的距平进行对比，结果表明，对于每一个参数而言，其距平随时间和空间变化，Vm、Dz和e的距平在冬半年为正值，在夏半年为负值，而Dp和Gm的距平在冬半年为负值，在夏半年为正值。5个参数的变化趋势符合物理意义和生态机制。
将模型中的参数分别按上述4种形式赋值，运行正向模式，模拟时间为1年。实验结果表明考虑参数时空分布的实验误差最小。说明在海洋生态系统动力学数值模拟中，与只考虑参数的空间分布、只考虑参数的时间分布以及把参数看作不随时空变化的常数相比，考虑参数时空分布更合理，有利于提高模拟精度；伴随同化技术在优化时空变化的参数方面，是一种有效的，值得推广的方法，它为我们研究生态系统的变化机制、对生态系统进行模拟和预报提供科学的决策依据。
Advancing our understanding of the structure and functioning of the global oceanecosystem, its major subsystems, and its response to physical forcing is the scientificresearcher's common goal, so that a capability can be developed to forecast theresponses of the marine ecosystem to global change. Developing the ecosystemdynamics model is becoming an important tool for studying the complicated marineenvironment. In most previous studies, the temporal and spatial variation of primaryproductivity and the concentration of ecological variables have been studied. Someresearches realize the spatial variations of the parameters, but the temporal variationsof key parameters are always ignored or not taken into account at all. In this study, thespatial and temporal variations of the parameters are realized, which improves thesimulation precision.
In this effort, the adjoint variational method is applied to a3D marine ecosystemmodel (NPZD-type) and its adjoint model, which are built on global scale based onclimatological environment provided by SODA. The numerical study and assimilationexperiments are implemented within a depth of200m.
In twin experiments, model-generated data of phytoplankton in the surface layerare served as fictitious observations. When the spatially varying Vm (maximumuptake rate of nutrient by phytoplankton) is estimated alone, new strategies aredesigned to optimize the step-length which is used to adjust the parameters preferablyand the assimilation efficiency is improved. On the condition that the same step isemployed, the reduced cost function (RCF), the mean absolute error of phytoplanktonin the surface layer (MAE) and the relative error (RE) of Vm between given andsimulated values decrease obviously compared with strategy in previous work. Based on the strategy above, how would the distribution schemes of spatial parameterizationand influence radius affect the results is discussed. The simulation precision is thehighest when the rate of dependent grid distance to influence radius is1.6, whichprovides for future experiments. The influence of time step was studied then and it isfound that the assimilation recovery would not be more successful with a smaller timestep of3hours compared with6hours. So6hours is the better option, by which thecomputational efficiency is improved. On the basis of the above work, when the fivekey parameters (KP) were estimated simultaneously, the given spatial variations couldbe reproduced, and the REs are less than6%. Analysis of the results of twinexperiments by linear regression method demonstrates that the relationship betweenRE of parameters and MAE is direct ratio with a correlation coefficient of0.8, soMAE can be considered as a criterion to evaluate both simulation results andparameter estimation which is useful in practical application.
Real experiments are conducted based on the conclusions above.16°N-44°N,173°E-142°W and16°N-44°N,167°W-122°W are selected as study area. One year isdivided into72periods, each of which is five days long. Spatio-temporal variation ofKP was optimized by assimilating phytoplankton data in the surface layer in eachstudy area. For each study area, the RCF and MAE in each assimilation perioddecrease obviously after assimilation. The spatially varying KP (KPS), temporallyvarying KP (KPT) and constant KP (KPC) are obtained by averaging KP of spatialand temporal variation respectively. Another type of spatio-temporal KP (KPST) isrepresented by KPS, KPT and KPC. After the correlation analysis of KP, either KPS orKPT, it is found that there is the same distribution characteristics and variation trendbetween Vm, Dz and e. The correlation coefficient can reach0.99, and the relationbetween Dp and Gm is versa. After the comparison of KPT in the two study area, it isfound that KPT anomaly is time-varying. The anomaly of Vm, Dz and e are positivevalue in winter half year and negative value in summer half year, and the anomaly ofDp and Gm is versa, which accords with the real ecological mechanism.
The model is run with KPS, KPT, KPC, and KPST respectively, and it is found that MAE is the minimum when KP are spatio-temporal variation (KPST), whileMAE reaches its maximum when KP are constant (KPC). KPST, representation ofspatio-temporal variation, reduces the variable number in model calculation.Therefore the spatio-temporal variation of parameters, which is the focus of severalresearchers, is reasonable and necessary and the adjoint variational method is a usefultool for optimizing the spatio-temporal parameters in a dynamical marine ecosystemmodel.
引文
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