基于过程模型CROBAS的全局灵敏度分析方法比较

过程机理模型在开发过程中常受限于生理学参数无法直接或准确测量。全局灵敏度分析可以评估模型预测结果对于生理学参数变化的响应,为模型结构改进、数据收集和参数校准提供参考。本研究基于过程模型CROBAS,以华山松为例,选取模型中描述树木结构关系的10个参数,以树高和各器官生物量的Nash-Sutcliffe效率(NSE)为目标函数,比较了3种应用较广泛的全局灵敏度分析方法,即Morris筛选法、基于方差的Sobol指数法和扩展的傅里叶幅度检验法(EFAST)。结果表明: 参数灵敏度排序在不同方法中仅略微有所变化,但对于不同目标函数则区别明显。对算法耗时和收敛效率而言,Morris和EFAST性能较高,Sobol效率相对较低。所有模型输出变量均对单位面积年最大光合速率、比叶面积、消光系数敏感,林冠光截留状态对于林木生长量有着关键性影响,意味着光合固碳量是CROBAS在模型校正和林木生长动态模拟中需要优先进行数据收集、验证与测试的模块。灵敏度分析同时表明,碳平衡理论在林木生物量模拟中最为核心部分是树叶生物量模块的计算与验证。对于复杂过程模型的参数灵敏度分析,如需定性研究可选Morris,而量化评估采用EFAST更适合。     

基于全局灵敏度分析的浒苔生长影响参数研究

近年来,以浒苔为主的绿潮灾害频发。构建了浒苔生长模型,以定量分析浒苔生长过程,探索浒苔爆发机理。参数不确定性是模型不确定性的主要来源,以参数灵敏度分析为基础的参数优化有利于提高模型精度,采用Morris方法对模型涉及的主要参数进行了全局灵敏度分析,以研究浒苔生长的主要影响参数。不同于其他有关大型绿藻的模型模拟,模型同时考虑了幼体浒苔和成熟浒苔的生物量变化,并修正了营养盐限制函数以及温度计算函数。全局性的参数灵敏度分析结果表明,最适温度(T_(opt))、光合作用最适光强(Is)、最大发芽率(G_(max))、浒苔生长所需的氮含量的半饱和系数(kqn)、最大氮摄取率(V_(maxn))这5个参数在浒苔生长模型中具有较大灵敏性。其中,T_(opt)影响最大,Is和V_(maxn)其次,说明浒苔生长主要受温度光照和氮含量限制。相较于局部灵敏度分析仅关注单个参数变化、依赖于初值选取等缺陷,全局灵敏度分析同时从各个参数的取值范围上分析参数对模型结果的影响,能揭示参数之间相互作用的影响。此外,灵敏度较大的参数往往和其他参数之间存在较大相关性。     

Testing parameter sensitivities and uncertainty analysis of Biome-BGC model in simulating carbon and water fluxes in broadleaved-Korean pine forests

生态过程模型的发展为研究者在长时间序列和区域尺度的研究提供了便利, 但模型模拟的准确性受到模型自身结构、模型参数估计合理性的影响。敏感性分析能够定量或定性筛选出对模型模拟结果影响较大的敏感参数, 是模型参数校准过程中的重要工具, 也是建模和应用的先决条件。该文以阔叶红松林为研究对象, 采用全局敏感性分析方法——傅里叶幅度灵敏度检验扩展法(EFAST)对Biome-BGC模型的生理生态参数进行了敏感性分析, 分别分析了红松(Pinus koraiensis)和阔叶树的净初级生产力(NPP)、蒸散(ET)对参数变化的敏感性。结果表明: (1)模拟红松NPP的不确定性高于阔叶树, 但二者的模拟ET的不确定性均较小。阔叶树的NPP和ET对生理生态参数的敏感性总体上都小于红松。(2)无论是红松、阔叶或其他植被类型, 模拟NPP均表现出对叶片碳氮比、细根碳氮比、比叶面积(SLA)和冠层截留系数的敏感性, 这4个参数的高敏感性主要是由模型自身结构所决定的, 与植被类型和研究地区的关系较小。对模拟ET而言, 细根与叶片碳分配比、新茎与新叶碳分配比和SLA均是影响红松和阔叶树ET的敏感参数, 但红松ET主要受参数与参数间的二阶或多阶交互作用的间接影响, 而阔叶树ET则主要是受到敏感参数直接效应的影响。(3)除了上述影响红松和阔叶树碳水通量的共性参数外, 诸如核酮糖-1,5-二磷酸羧化酶中叶氮含量、叶片与细根周转率、所有叶面积与投影叶面积之比等也是对模拟结果有影响的重要参数, 但是其敏感程度随物种不同和研究区不同而不同, 所以这类参数可以根据具体情况进行参数本地化, 对于其他不敏感参数则可以采用模型缺省值。     

Biome-BGC模型模拟阔叶红松林碳水通量的参数敏感性检验和不确定性分析

生态过程模型的发展为研究者在长时间序列和区域尺度的研究提供了便利, 但模型模拟的准确性受到模型自身结构、模型参数估计合理性的影响。敏感性分析能够定量或定性筛选出对模型模拟结果影响较大的敏感参数, 是模型参数校准过程中的重要工具, 也是建模和应用的先决条件。该文以阔叶红松林为研究对象, 采用全局敏感性分析方法——傅里叶幅度灵敏度检验扩展法(EFAST)对Biome-BGC模型的生理生态参数进行了敏感性分析, 分别分析了红松(Pinus koraiensis)和阔叶树的净初级生产力(NPP)、蒸散(ET)对参数变化的敏感性。结果表明: (1)模拟红松NPP的不确定性高于阔叶树, 但二者的模拟ET的不确定性均较小。阔叶树的NPP和ET对生理生态参数的敏感性总体上都小于红松。(2)无论是红松、阔叶或其他植被类型, 模拟NPP均表现出对叶片碳氮比、细根碳氮比、比叶面积(SLA)和冠层截留系数的敏感性, 这4个参数的高敏感性主要是由模型自身结构所决定的, 与植被类型和研究地区的关系较小。对模拟ET而言, 细根与叶片碳分配比、新茎与新叶碳分配比和SLA均是影响红松和阔叶树ET的敏感参数, 但红松ET主要受参数与参数间的二阶或多阶交互作用的间接影响, 而阔叶树ET则主要是受到敏感参数直接效应的影响。(3)除了上述影响红松和阔叶树碳水通量的共性参数外, 诸如核酮糖-1,5-二磷酸羧化酶中叶氮含量、叶片与细根周转率、所有叶面积与投影叶面积之比等也是对模拟结果有影响的重要参数, 但是其敏感程度随物种不同和研究区不同而不同, 所以这类参数可以根据具体情况进行参数本地化, 对于其他不敏感参数则可以采用模型缺省值。     

浑太流域实际蒸散的时空变化特征及影响因素

基于浑太流域1970—2006年气象、水文资料,采用参数率定后的平流-干旱（AA）模型计算浑太流域蒸散.根据水量平衡法得到的蒸散结果对模型的原始参数进行调整,并在4个子流域进行验证.采用线性趋势分析、滑动平均法、克里金插值、灵敏度分析方法研究浑太流域蒸散的时空变化和影响因素.结果表明： AA模型经验参数（0.75）在浑太流域上的计算误差为11.4%,表明AA模型在浑太流域上是可行的;浑太流域年均蒸散量为347.4 mm,并以1.58 mm·(10 a)^-1的速率略呈上升趋势,但上升趋势不明显,年内呈单峰变化,峰值出现在7月;季节变化上,夏季最大,冬季最小,春季高于秋季;整个流域实际蒸散量呈现从西北至东南逐渐减少的分布特征,但差异不大;净辐射是影响浑太流域蒸散变化的主导因素.
     

稻田甲烷排放模型研究——模型灵敏度分析

模型方法对区域稻田甲烷排放估计的不确定性主要源于模型参数在区域范围内的误差,这种误差导致的估计不确定性由模型灵敏度决定.采用一种动力学分析与统计分析相结合的方法对稻田甲烷模型CH4MOD进行了参数灵敏度分析,结果表明,稻田水管理方式的灵敏度最高,灵敏度指数为O.64,其次为稻田土壤的砂粒含量参数,灵敏度指数0.50,灵敏度最低的参数是水稻移栽期地上生物量.以模型灵敏度指数为基础,建立了模型估计值不确定性与模型参数区域化误差间的数量关系,利用这一量化关系得出我国2000年稻田甲烷排放的不确定性范围为3.09～10.61Tg.此外,模型灵敏度参数的大小也反映了模型要素对稻田甲烷排放影响的大小,因而分析的结果对于采取合理措施减少稻田甲烷排放具有指导意义.     

胶州湾生物-物理耦合模型参数灵敏度分析

参数灵敏度分析旨在评价模型中各参数对模拟结果的影响程度,是参数优化和模型校正的基础步骤,也是认识模型行为的重要工具。所建的胶州湾生物-物理耦合模型包括浮游植物、浮游动物、营养盐、碎屑和溶解氧5类状态变量,对其涉及的50个参数进行灵敏度分析,得到3个非常灵敏性参数、2个灵敏性参数、11个比较灵敏性参数和34个不太灵敏性参数。非常灵敏及灵敏性参数包括浮游植物生长速率(μPRPC)、暗反应修正因子(FAC)、光饱和强度(α)、浮游植物死亡率(μDEPC)和水体消光系数(bla),主要影响浮游植物生长和死亡过程,反映了浮游植物在生态系统中的基础性和重要性作用。这5个参数显著地影响碳和营养盐循环,是整个胶州湾生态系统最主要的影响参数,应优先进行优化。比较灵敏性参数的影响主要表现在营养盐对浮游植物生长或死亡的限制以及温度对光饱和量的限制,浮游动物生长、牧食和死亡过程以及浮游植物生物量对牧食的限制,叶绿素a的生产,缺氧条件下沉积物释放磷以及浮游植物对磷的摄取等过程,这些参数对于各状态变量的灵敏性存在不同程度的差异,从而表征不同的特点。与不太灵敏性参数相关的过程主要为叶绿素a和碎屑消光作用,温度对浮游植物生长、浮游动物牧食、碎屑和沉积物矿化的限制,碎屑和沉积物矿化与沉降,与无机氮相关的大部分过程,溶解氧浓度变化等,这些过程除了受模型内部参数影响外,还在很大程度上受水深、海水温度和陆源污染等外部因素影响。比较灵敏及不太灵敏性参数影响模型局部过程,是模型校正的重要依据,除了非常灵敏及灵敏性参数以外,叶绿素a、浮游动物、碎屑和无机磷四种状态变量可分别根据叶绿素a最大生产系数(K CHmax)、浮游动物一级死亡率(μDEZC1)、有机碎屑矿化率(μREDC)和浮游植物磷摄取的半饱和常数(h UPPP)进行校正。与营养盐相关参数的灵敏度分析表明,胶州湾浮游植物处于磷限制,无机氮主要受陆源排污影响。因此,对无机氮的校正主要通过合理设置沿岸河流径流量或陆源污染物浓度与比例以及无机氮初始场。溶解氧对各参数均不太灵敏。     

ROC曲线形状在生态位模型评价中的重要性——以美国白蛾为例

【目的】生态位模型在生物地理学、入侵生物学和保护生物学中具有广泛的应用,被越来越多地用于预测物种潜在分布和现实分布的研究中。本文以美国白蛾为例介绍pROC方案在生态位模型评价中的应用及其注意事项,以期对物种潜在分布预测进行合理的评价,促进生态位模型在我国的合理运用和发展。【方法】介绍ROC曲线和AUC值基本原理,总结其在生态位模型评价中的应用,从物种存在分布点和不存在分布点的可信度出发,分析AUC值用于模型评价的优点和不足,最后介绍局部受试者工作特征曲线的线下面积方案(pROC方案)来弥补传统AUC值的不足。【结果】AUC值虽独立于阈值,但因其综合灵敏度和特异度,而屏蔽这2个指标各自的特征,不能分别评估预测结果的灵敏度和特异度,同时对遗漏率和记账错率不能进行权衡,会误导使用者对模型的评价。与AUC值相比,ROC曲线的形状更具有价值,蕴含丰富的模型评价信息。【结论】模型评价需要将灵敏度和特异度区别对待,ROC曲线形状比AUC值在生态位模型评价中更为重要,pROC方案相对于传统AUC值具有优势,但容易对过度模拟做出不当判断。模型评价与作者研究目的密切相关:当以预测物种潜在分布为目的时(如入侵物种潜在分布、气候变化对物种分布的影响和谱系生物地理学),模型评价应当给予灵敏度(或者遗漏率)更多的权重;当以预测物种现实分布为目的时(如保护区界定和濒危物种引入),模型评价应当给予灵敏度和特异度同等的权重。     

生物稳定塘碳、氮、磷物质迁移转化模型的研究

本研究较系统地在试验基础上建立了生物稳定塘系统内碳、氮、磷营养物质转移规律的生态学模型,并对模型进行了全面参数估值和估值的灵敏度分析,用实地塘数据对模型进行了检验。结果表明:模型结构合理,总体上能够反映碳、氮、磷在稳定塘正常运转条件下的迁移转化规律及塘内生物和生物化学反应的特征。模型参数适用,解法成功,具有广泛的应用前景。     

城市生态系统的模拟方法：灵敏度模型及其改进

评估城市生态系统的持续发展能力,探讨其持续发展对策是一个复杂的动态问题,需要运用动态的模拟方法进行。由德国著名生态控制论专家Ｆ．Ｖｅｓｔｅｒ和Ａ．Ｖ．Ｈｅｓｌｅｒ教授提出的“灵敏度模型”方法,将系统科学思想、生态控制论方法及城市规划融为一体,解释、模拟、评价和规划城市复杂的系统关系,是模拟城市生态系统很好的方法。本文对该方法进行了改进。改进后的“灵敏度模型”为评价城市持续发展能力、探讨其持续发展对策提供了新的思路。     

Evaluating the Use of Global Sensitivity Analysis in Dynamic MFA

Dynamic material flow analysis (MFA) provides information about material usage over time and consequent changes in material stocks and flows. In order to understand the effect of limited data quality and model assumptions on MFA results, the use of sensitivity analysis methods in dynamic MFA studies has been on the increase. So far, sensitivity analysis in dynamic MFA has been conducted by means of a one‐at‐a‐time method, which tests parameter perturbations individually and observes the outcomes on output. In contrast to that, variance‐based global sensitivity analysis decomposes the variance of the model output into fractions caused by the uncertainty or variability of input parameters. The present study investigates interaction and time‐delay effects of uncertain parameters on the output of an archetypal input‐driven dynamic material flow model using variance‐based global sensitivity analysis. The results show that determining the main (first‐order) effects of parameter variations is often sufficient in dynamic MFA because substantial effects attributed to the simultaneous variation of several parameters (higher‐order effects) do not appear for classical setups of dynamic material flow models. For models with time‐varying parameters, time‐delay effects of parameter variation on model outputs need to be considered, potentially boosting the computational cost of global sensitivity analysis. Finally, the implications of exploring the sensitivities of model outputs with respect to parameter variations in the archetypical model are used to derive model‐ and goal‐specific recommendations on choosing appropriate sensitivity analysis methods in dynamic MFA.     

Sensitivity Analysis of an ENteric Immunity SImulator (ENISI)-Based Model of Immune Responses to Helicobacter pylori Infection

Agent-based models (ABM) are widely used to study immune systems, providing a procedural and interactive view of the underlying system. The interaction of components and the behavior of individual objects is described procedurally as a function of the internal states and the local interactions, which are often stochastic in nature. Such models typically have complex structures and consist of a large number of modeling parameters. Determining the key modeling parameters which govern the outcomes of the system is very challenging. Sensitivity analysis plays a vital role in quantifying the impact of modeling parameters in massively interacting systems, including large complex ABM. The high computational cost of executing simulations impedes running experiments with exhaustive parameter settings. Existing techniques of analyzing such a complex system typically focus on local sensitivity analysis, i.e. one parameter at a time, or a close “neighborhood” of particular parameter settings. However, such methods are not adequate to measure the uncertainty and sensitivity of parameters accurately because they overlook the global impacts of parameters on the system. In this article, we develop novel experimental design and analysis techniques to perform both global and local sensitivity analysis of large-scale ABMs. The proposed method can efficiently identify the most significant parameters and quantify their contributions to outcomes of the system. We demonstrate the proposed methodology for ENteric Immune SImulator (ENISI), a large-scale ABM environment, using a computational model of immune responses to Helicobacter pylori colonization of the gastric mucosa.     

Sensitivity analysis of Repast computational ecology models with R/Repast

Computational ecology is an emerging interdisciplinary discipline founded mainly on modeling and simulation methods for studying ecological systems. Among the existing modeling formalisms, the individual‐based modeling is particularly well suited for capturing the complex temporal and spatial dynamics as well as the nonlinearities arising in ecosystems, communities, or populations due to individual variability. In addition, being a bottom‐up approach, it is useful for providing new insights on the local mechanisms which are generating some observed global dynamics. Of course, no conclusions about model results could be taken seriously if they are based on a single model execution and they are not analyzed carefully. Therefore, a sound methodology should always be used for underpinning the interpretation of model results. The sensitivity analysis is a methodology for quantitatively assessing the effect of input uncertainty in the simulation output which should be incorporated compulsorily to every work based on in‐silico experimental setup. In this article, we present R/Repast a GNU R package for running and analyzing Repast Simphony models accompanied by two worked examples on how to perform global sensitivity analysis and how to interpret the results.     

Comparative study of parameter sensitivity analyses of the TCR-activated Erk-MAPK signalling pathway

Parameter estimation is a major challenge for mathematical modelling of biological systems. Given the uncertainties associated with model parameters, it is important to understand how sensitive the model output is to variations in parameter values. A local sensitivity analysis determines the model sensitivity to parameter variations over a localised region around the nominal parameter values, whereas a global sensitivity analysis (GSA) investigates the sensitivity over the entire parameter space. Using a T-cell receptor-activated Erk-MAPK signalling pathway model as an example, the authors present a comparative study of a variety of different sensitivity analysis techniques. These techniques include: local sensitivity analysis, existing GSA methods of partial rank correlation coefficient, Sobol's, extended Fourier amplitude sensitivity test, as well as a weighted average of local sensitivities and a new GSA method to extract global parameter sensitivities from a parameter identification routine. Results of this study revealed critical reactions in the signalling pathway and their impact on the signalling dynamics and provided insights into embedded regulatory mechanisms such as feedback loops in the pathway. From this study, a recommendation emerges for a general sensitivity analysis strategy to efficiently and reliably infer quantitative, dynamic as well as topological properties from systems biology models.     

Evaluation of habitat suitability index models by global sensitivity and uncertainty analyses: a case study for submerged aquatic vegetation

Habitat suitability index (HSI) models are commonly used to predict habitat quality and species distributions and are used to develop biological surveys, assess reserve and management priorities, and anticipate possible change under different management or climate change scenarios. Important management decisions may be based on model results, often without a clear understanding of the level of uncertainty associated with model outputs. We present an integrated methodology to assess the propagation of uncertainty from both inputs and structure of the HSI models on model outputs (uncertainty analysis: UA) and relative importance of uncertain model inputs and their interactions on the model output uncertainty (global sensitivity analysis: GSA). We illustrate the GSA/UA framework using simulated hydrology input data from a hydrodynamic model representing sea level changes and HSI models for two species of submerged aquatic vegetation (SAV) in southwest Everglades National Park: Vallisneria americana (tape grass) and Halodule wrightii (shoal grass). We found considerable spatial variation in uncertainty for both species, but distributions of HSI scores still allowed discrimination of sites with good versus poor conditions. Ranking of input parameter sensitivities also varied spatially for both species, with high habitat quality sites showing higher sensitivity to different parameters than low‐quality sites. HSI models may be especially useful when species distribution data are unavailable, providing means of exploiting widely available environmental datasets to model past, current, and future habitat conditions. The GSA/UA approach provides a general method for better understanding HSI model dynamics, the spatial and temporal variation in uncertainties, and the parameters that contribute most to model uncertainty. Including an uncertainty and sensitivity analysis in modeling efforts as part of the decision‐making framework will result in better‐informed, more robust decisions.     

基于BIOME-BGC模型的长白落叶松林净初级生产力模拟参数敏感性

基于植被生理生态过程的模型包含较多参数,合理的参数取值能够极大地提高模型的模拟能力.参数敏感性分析可以全面分析模型参数对模拟结果的影响程度,在筛选模型敏感参数过程中起到重要作用.本研究以模拟吉林省汪清林业局长白落叶松林净初级生产力（NPP）为例,分析了BIOME-BGC模型的参数敏感性.首先利用样地实测NPP数据与模拟值进行对比分析,检验模型对长白落叶松林NPP的模拟能力;然后利用Morris法和EFAST法筛选出BIOME-BGC模型中对长白落叶松林NPP影响较大的敏感参数.在此基础上,通过EFAST法对所有筛选出的参数进行定量的敏感性分析,计算了敏感参数的全局敏感性指数、一阶敏感性指数和二阶敏感性指数.结果表明： BIOME-BGC模型能够较好地模拟研究区内长白落叶松林NPP的变化趋势;Morris法可以在样本量较少的情况下实现对BIOME-BGC模型敏感参数的筛选,而EFAST法可以定量分析BIOME-BGC模型中单个参数以及不同参数之间交互作用对模拟结果的影响程度;BIOME-BGC模型中对长白落叶松林NPP影响较大的敏感参数为新生茎与叶片的碳分配比和叶片碳氮比,且二者之间的交互作用明显大于其他参数之间的交互作用.     

The importance of assessing parameter sensitivity when using biophysical models: a case study using plethodontid salamanders

Landscapes are continually changing due to numerous assaults, including habitat alteration, anthropogenic disturbances, and climate change. Understanding how species will respond to these changes is of critical importance for conservation and management. Mechanistic models, such as biophysical models (BPMs), are an increasingly popular tool to predict how local population dynamics or species’ distributions may be altered in response to environmental and climate changes. By mechanistically modeling relationships between environmental conditions, physiology and behavior, it is possible to make accurate predictions about how species may respond. However, BPMs are often difficult to implement due to lack of appropriate, species-specific data that is biologically realistic or relevant. In this study, we present a BPM for the salamander Plethodon jordani and assess how adding more biological realism has potential to alter model predictions about annual energy budgets. Additionally, we conducted local and global sensitivity analyses to evaluate the importance of accurately specifying model parameter values and functional relationships. We found that the addition of biological realism resulted in greater model complexity as well as substantially different estimates of energy balance. Correct parameterization of biophysical models is also critical, as small changes in parameter values can result in disproportionately large changes in downstream model estimates. Our model highlights the overall importance of using ecologically relevant and specific data for input parameters, as well as careful assessment of parameter sensitivity. We encourage researchers to be aware of the data they are using to parameterize BPMs, and urge the collection of system-specific data that is relevant in spatial and temporal scale. We also recommend greater and more transparent use of sensitivity analyses to provide a better understanding of the model, as well as greater confidence in model predictions.     

Sensitivity Analysis in Multicriteria Spatial Decision-Making: A Review

The aim of this article is to review how sensitivity analysis has been applied to models based on Geographical Information Systems (GIS) and Multicriteria Evaluation techniques (MCE). This kind of analysis is conceived as a stage in the model evaluation that examines the extent of output variation of a model when parameters are systematically varied over a range of interest. Twenty-eight studies related to land planning processes, environmental management, and location of noxious facilities have been examined. This review reveals that sensitivity analysis is a) not a common practice, b) is more widely carried out in location of noxious facilities, and c) that the analysis most frequently used is based on the variation of the weights of the factors implied in the process to test whether it significantly modifies the results obtained.     

Parameter optimization and sensitivity analysis for large kinetic models using a real-coded genetic algorithm

Dynamic modeling is a powerful tool for predicting changes in metabolic regulation. However, a large number of input parameters, including kinetic constants and initial metabolite concentrations, are required to construct a kinetic model. Therefore, it is important not only to optimize the kinetic parameters, but also to investigate the effects of their perturbations on the overall system. We investigated the efficiency of the use of a real-coded genetic algorithm (RCGA) for parameter optimization and sensitivity analysis in the case of a large kinetic model involving glycolysis and the pentose phosphate pathway in Escherichia coli K-12. Sensitivity analysis of the kinetic model using an RCGA demonstrated that the input parameter values had different effects on model outputs. The results showed highly influential parameters in the model and their allowable ranges for maintaining metabolite-level stability. Furthermore, it was revealed that changes in these influential parameters may complement one another. This study presents an efficient approach based on the use of an RCGA for optimizing and analyzing parameters in large kinetic models.