Parameter sensitivity analysis for a biochemically-based photosynthesis model

A challenge for the development of Land Surface Models(LSMs) is improving transpiration of water exchange and photosynthesis of carbon exchange between terrestrial plants and the atmosphere, both of which are governed by stoma in leaves. In the photosynthesis module of these LSMs, variations of parameters arising from diversity in plant functional types(PFTs) and climate remain unclear. Identifying sensitive parameters among all photosynthetic parameters before parameter estimation can not only reduce operation cost, but also improve the usability of photosynthesis models worldwide. Here, we analyzed 13 parameters of a biochemically-based photosynthesis model(FvCB), implemented in many LSMs, using two sensitivity analysis(SA) methods(i.e., the Sobol’ method and the Morris method) for setting up the parameter ensemble. Three different model performance metrics, i.e.,Root Mean Squared Error(RMSE), Nash Sutcliffe efficiency(NSE), and Standard Deviation(STDEV) were introduced for model assessment and sensitive parameters identification. The results showed that among all photosynthetic parameters only a small portion of parameters were sensitive, and the sensitive parameters were different across plant functional types: maximum rate of Rubisco activity(Vcmax25), maximum electron transport rate(Jmax25), triose phosphate use rate(TPU) and dark respiration in light(Rd) were sensitive in broad leafevergreen trees(BET), broad leaf-deciduous trees(BDT) and needle leaf-evergreen trees(NET), while only Vcmax25and TPU are sensitive in short vegetation(SV), dwarf trees and shrubs(DTS), and agriculture and grassland(AG). The two sensitivity analysis methods suggested a strong SA coherence;in contrast, different model performance metrics led to different SA results. This misfit suggests that more accurate values of sensitive parameters, specifically, species specific and seasonal variable parameters, are required to improve the performance of the FvCB model.

Parameter identification and global sensitivity analysis of Xin'anjiang model using meta-modeling approach

Parameter identification, model calibration, and uncertainty quantification are important steps in the model-building process, and are necessary for obtaining credible results and valuable information. Sensitivity analysis of hydrological model is a key step in model uncertainty quantification, which can identify the dominant parameters, reduce the model calibration uncertainty, and enhance the model optimization efficiency. There are, however, some shortcomings in classical approaches, including the long duration of time and high computation cost required to quantitatively assess the sensitivity of a multiple-parameter hydrological model. For this reason, a two-step statistical evaluation framework using global techniques is presented. It is based on （1） a screening method （Morris） for qualitative ranking of parameters, and （2） a variance-based method integrated with a meta-model for quantitative sensitivity analysis, i.e., the Sobol method integrated with the response surface model （RSMSobol）. First, the Morris screening method was used to qualitatively identify the parameters＇ sensitivity, and then ten parameters were selected to quantify the sensitivity indices. Subsequently, the RSMSobol method was used to quantify the sensitivity, i.e., the first-order and total sensitivity indices based on the response surface model （RSM） were calculated. The RSMSobol method can not only quantify the sensitivity, but also reduce the computational cost, with good accuracy compared to the classical approaches. This approach will be effective and reliable in the global sensitivity analysis of a complex large-scale distributed hydrological model.

Second-Order Adjoint Sensitivity Analysis Methodology for Computing Exactly Response Sensitivities to Uncertain Parameters and Boundaries of Linear Systems: Mathematical Framework

This work presents the “Second-Order Comprehensive Adjoint Sensitivity Analysis Methodology (2nd-CASAM)” for the efficient and exact computation of 1st- and 2nd-order response sensitivities to uncertain parameters and domain boundaries of linear systems. The model’s response (i.e., model result of interest) is a generic nonlinear function of the model’s forward and adjoint state functions, and also depends on the imprecisely known boundaries and model parameters. In the practically important particular case when the response is a scalar-valued functional of the forward and adjoint state functions characterizing a model comprising N parameters, the 2nd-CASAM requires a single large-scale computation using the First-Level Adjoint Sensitivity System (1st-LASS) for obtaining all of the first-order response sensitivities, and at most N large-scale computations using the Second-Level Adjoint Sensitivity System (2nd-LASS) for obtaining exactly all of the second-order response sensitivities. In contradistinction, forward other methods would require (N2/2 + 3 N/2) large-scale computations for obtaining all of the first- and second-order sensitivities. This work also shows that constructing and solving the 2nd-LASS requires very little additional effort beyond the construction of the 1st-LASS needed for computing the first-order sensitivities. Solving the equations underlying the 1st-LASS and 2nd-LASS requires the same computational solvers as needed for solving (i.e., “inverting”) either the forward or the adjoint linear operators underlying the initial model. Therefore, the same computer software and “solvers” used for solving the original system of equations can also be used for solving the 1st-LASS and the 2nd-LASS. Since neither the 1st-LASS nor the 2nd-LASS involves any differentials of the operators underlying the original system, the 1st-LASS is designated as a “first-level” (as opposed to a “first-order”) adjoint sensitivity system, while the 2nd-LASS is designated as a “second-level” (rather than a “second-order”) adjoint sensitivity system. Mixed second-order response sensitivities involving boundary parameters may arise from all source terms of the 2nd-LASS that involve the imprecisely known boundary parameters. Notably, the 2nd-LASS encompasses an automatic, inherent, and independent “solution verification” mechanism of the correctness and accuracy of the 2nd-level adjoint functions needed for the efficient and exact computation of the second-order sensitivities.

Parameters Sensitivity Analysis and Correction for Concrete Damage Plastic Model

In order to understand the effect of hardening ductility parameters and softening ductility parameters of the concrete damage plastic model in LS-DYNA,a sensitivity and reliability analysis of these parameters through a convenient cube unit test was conducted. The results showed that the peak strength strain was independent of the hardening ductility parameter DH,but affected by AH,BH,and CH. The softening ductility was mainly related to the softening ductility parameter AS,but not affected by the damage ductility exponent BS. In case that the model with default parameters failed to match the AS-controlled damage softening phase,an optimized model with an AS correction was developed. The corrected model with the AS value of 2 matched well with the code model,and exhibited good feasibility in predicting the stress-strain curve of different grades of concrete. Moreover,the practicability of the corrected model was further validated by the conventional triaxial test. The simulated curve exhibited favorable consistence with the trial curve. Therefore,the model with parameter correction could provide a prospective reference for predicting the mechanical properties of concrete.

Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N): II. Paradigm Application to a Bernoulli Model Comprising Uncertain Parameters

This work presents the application of the recently developed “Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N)” to a simplified Bernoulli model. The 5th-CASAM-N builds upon and incorporates all of the lower-order (i.e., the first-, second-, third-, and fourth-order) adjoint sensitivities analysis methodologies. The Bernoulli model comprises a nonlinear model response, uncertain model parameters, uncertain model domain boundaries and uncertain model boundary conditions, admitting closed-form explicit expressions for the response sensitivities of all orders. Illustrating the specific mechanisms and advantages of applying the 5th-CASAM-N for the computation of the response sensitivities with respect to the uncertain parameters and boundaries reveals that the 5th-CASAM-N provides a fundamental step towards overcoming the curse of dimensionality in sensitivity and uncertainty analysis.

A New Sensitivity Analysis Approach Using Conditional Nonlinear Optimal Perturbations and Its Preliminary Application

Simulations and predictions using numerical models show considerable uncertainties,and parameter uncertainty is one of the most important sources.It is impractical to improve the simulation and prediction abilities by reducing the uncertainties of all parameters.Therefore,identifying the sensitive parameters or parameter combinations is crucial.This study proposes a novel approach:conditional nonlinear optimal perturbations sensitivity analysis(CNOPSA)method.The CNOPSA method fully considers the nonlinear synergistic effects of parameters in the whole parameter space and quantitatively estimates the maximum effects of parameter uncertainties,prone to extreme events.Results of the analytical g-function test indicate that the CNOPSA method can effectively identify the sensitivity of variables.Numerical results of the theoretical five-variable grassland ecosystem model show that the maximum influence of the simulated wilted biomass caused by parameter uncertainty can be estimated and computed by employing the CNOPSA method.The identified sensitive parameters can easily change the simulation or prediction of the wilted biomass,which affects the transformation of the grassland state in the grassland ecosystem.The variance-based approach may underestimate the parameter sensitivity because it only considers the influence of limited parameter samples from a statistical view.This study verifies that the CNOPSA method is effective and feasible for exploring the important and sensitive physical parameters or parameter combinations in numerical models.

Global sensitivity analysis for choosing the main soil parameters of a crop model to be determined

The use of a crop model like STICS for appropriate management decision support requires a good knowledge of all the parameters of the model. Among them, the soil parameters are difficult to know at each point of interest and costly techniques may be used to measure them. It is therefore important to know which soil parameters need to be determined. It can be stated that those which affect significantly the output variable deserve an accurate determination while those which slightly affect the model output variable do not. This paper demonstrates how a global sensitivity analysis method based on variance decomposition can be applied on soil parameters in order to divide them in the two categories. The Extended FAST method applied to the crop model STICS and a set of 13 soil parameters first allows to calculate the part of variance explained by each soil parameter (giving global sensitivity indices of the soil parameters) and the coefficient of variation of the output variables (measuring the effect of the parameter uncertainty on each variable). These metrics are therefore used for deciding on the importance of the parameter value measurement. Different output variables (Leaf Area Index and chlorophyll content) are evaluated at different stages of interest while others (crop yield, grain protein content, soil mineral nitrogen) are evaluated at harvest. The analysis is applied on two different annual crops (wheat and sugar beet), two contrasted weather and two types of soil depth. When the uncertainty of the output generated by the soil parameters is large (coefficient of variation > 1/3), only the parameters having a significant global sensitivity indices (higher than 10%) are retained. The results show that the number of soil parameters which deserve an accurate determination can be significantly reduced by the use of this relevant method for appropriate management decision support.

The First-Order Comprehensive Sensitivity Analysis Methodology (1st-CASAM) for Scalar-Valued Responses: I. Theory

This work presents the first-order comprehensive adjoint sensitivity analysis methodology (1st-CASAM) for computing efficiently, exactly, and exhaustively, the first-order sensitivities of scalar-valued responses (results of interest) of coupled nonlinear physical systems characterized by imprecisely known model parameters, boundaries and interfaces between the coupled systems. The 1st-CASAM highlights the conclusion that response sensitivities to the imprecisely known domain boundaries and interfaces can arise both from the definition of the system’s response as well as from the equations, interfaces and boundary conditions defining the model and its imprecisely known domain. By enabling, in premiere, the exact computations of sensitivities to interface and boundary parameters and conditions, the 1st-CASAM enables the quantification of the effects of manufacturing tolerances on the responses of physical and engineering systems. Ongoing research will generalize the methodology presented in this work, aiming at computing exactly and efficiently higher-order response sensitivities for coupled systems involving imprecisely known interfaces, parameters, and boundaries.

The First-Order Comprehensive Sensitivity Analysis Methodology (1^st-CASAM) for Scalar-Valued Responses: II. Illustrative Application to a Heat Transport Benchmark Model

This work illustrates the application of the 1st-CASAM to a paradigm heat transport model which admits exact closed-form solutions. The closed-form expressions obtained in this work for the sensitivities of the temperature distributions within the model to the model’s parameters, internal interfaces and external boundaries can be used to benchmark commercial and production software packages for simulating heat transport. The 1st-CASAM highlights the novel finding that response sensitivities to the imprecisely known domain boundaries and interfaces can arise both from the definition of the system’s response as well as from the equations, interfaces and boundary conditions that characterize the model and its imprecisely known domain. By enabling, in premiere, the exact computations of sensitivities to interface and boundary parameters and conditions, the 1st-CASAM enables the quantification of the effects of manufacturing tolerances on the responses of physical and engineering systems.

Global sensitivity analysis of the AquaCrop model for winter wheat under different water treatments based on the extended Fourier amplitude sensitivity test

Sensitivity analysis （SA） is an effective tool for studying crop models; it is an important link in model localization and plays an important role in crop model calibration and application. The objectives were to （i） determine influential and non-influential parameters with respect to above ground biomass （AGB）, canopy cover （CC）, and grain yield of winter wheat in the Beijing area based on the AquaCrop model under different water treatments （rainfall, normal irrigation, and over-irrigation）; and （ii） generate an AquaCrop model that can be used in the Beijing area by setting non-influential parameters to fixed values and adjusting influential parameters according to the SA results. In this study, field experiments were conducted during the 2012-2013,2013-2014, and 2014-2015 winter wheat growing seasons at the National Precision Agriculture Demonstration Research Base in Beijing, China. The extended Fourier amplitude sensitivity test （EFAST） method was used to perform SA of the AquaCrop model using 42 crop parameters, in order to verify the SA results, data from the 2013-2014 growing season were used to calibrate the AquaCrop model, and data from 2012-2013 and 2014-2015 growing seasons were val- idated. For AGB and yield of winter wheat, the total order sensitivity analysis had more sensitive parameters than the first order sensitivity analysis. For the AGB time-series, parameter sensitivity was changed under different water treatments; in comparison with the non-stressful conditions （normal irrigation and over-irrigation）, there were more sensitive parameters under water stress （rainfall）, while root development parameters were more sensitive. For CC with time-series and yield, there were more sensitive parameters under water stress than under no water stress. Two parameters sets were selected to calibrate the AquaCrop model, one group of parameters were under water stress, and the others were under no water stress, there were two more sensitive parameters （growing degree-days （GDD） from sowing to the maximum rooting depth （root） and the maximum effective rooting depth （rtx）） under water stress than under no water stress. The results showed that there was higher accuracy under water stress than under no water stress. This study provides guidelines for AquaCrop model calibration and application in Beijing, China, as well providing guidance to simplify the AquaCrop model and improve its precision, especially when many parameters are used.

Ranking parameters in urban energy models for various building forms and climates using sensitivity analysis

Urban Building Energy Modelling(UBEM)allows us to simulate buildings’energy performances at a larger scale.However,creating a reliable urban-scale energy model of new or existing urban areas can be difficult since the model requires overly detailed input data,which is not necessarily publicly unavailable.Model calibration is a necessary step to reduce the uncertainties and simulation results in order to develop a reliable and accurate UBEM.Due to the concerns over computational resources and the time needed for calibration,a sensitivity analysis is often required to identify the key parameters with the most substantial impact before the calibration is deployed in UBEM.Here,we study the sensitivity of uncertain input parameters that affect the annual heating and cooling energy demand by employing an urban-scale energy model,CitySim.Our goal is to determine the relative influence of each set of input parameters and their interactions on heating and cooling loads for various building forms under different climates.First,we conduct a global sensitivity analysis for annual cooling and heating consumption under different climate conditions.Building upon this,we investigate the changes in input sensitivity to different building forms,focusing on the indices with the largest Total-order sensitivity.Finally,we determine First-order indices and Total-order effects of each input parameter included in the urban building energy model.We also provide tables,showing the important parameters on the annual cooling and heating demand for each climate and each building form.We find that if the desired calibration process require to decrease the number of the inputs to save the computational time and cost,calibrating 5 parameters;temperature set-point,infiltration rate,floor U-value,avg.walls U-value and roof U-value would impact the results over 55%for any climate and any building form.

Sensitivity Analysis of Multi-phase Seepage Parameters Affecting the Clayey Silt Hydrate Reservoir Productivity in the Shenhu Area,South China Sea

Natural gas hydrate(NGH)is an important future resource for the 21st century and a strategic resource with potential for commercial development in the third energy transition.It is of great significance to accurately predict the productivity of hydrate-bearing sediments(HBS).The multi-phase seepage parameters of HBS include permeability,porosity,which is closely related to permeability,and hydrate saturation,which has a direct impact on hydrate content.Existing research has shown that these multi-phase seepage parameters have a great impact on HBS productivity.Permeability directly affects the transmission of pressure-drop and discharge of methane gas,porosity and initial hydrate saturation affect the amount of hydrate decomposition and transmission process of pressure-drop,and also indirectly affect temperature variation of the reservoir.Considering the spatial heterogeneity of multi-phase seepage parameters,a depressurization production model with layered heterogeneity is established based on the clayey silt hydrate reservoir at W11 station in the Shenhu Sea area of the South China Sea.Tough+Hydrate software was used to calculate the production model;the process of gas production and seepage parameter evolution under different multi-phase seepage conditions were obtained.A sensitivity analysis of the parameters affecting the reservoir productivity was conducted so that:(a)a HBS model with layered heterogeneity can better describe the transmission process of pressure and thermal compensation mechanism of hydrate reservoir;(b)considering the multi-phase seepage parameter heterogeneity,the influence degrees of the parameters on HBS productivity were permeability,porosity and initial hydrate saturation,in order from large to small,and the influence of permeability was significantly greater than that of other parameters;(c)the production potential of the clayey silt reservoir should not only be determined by hydrate content or seepage capacity,but also by the comprehensive effect of the two;and(d)time scales need to be considered when studying the effects of changes in multi-phase seepage parameters on HBS productivity.

Parameter Identification for Static Var Compensator Model Using Sensitivity Analysis and Improved Whale Optimization Algorithm

A parameter estimation method based on an improved Whale Optimization Algorithm is proposed in this paper to identify the parameters of a static var compensator(SVC)model.First,a mathematical model of SVC is established.Then,the reverse learning strategy and Levy flight disturbance strategy are introduced to improve the whale optimization algorithm,and the improved whale optimization algorithm is applied to the parameter identification of the static var compensator model.Finally,a stepwise identification method,by analyzing the local sensitivities of parameters,is proposed which solves the problem of low accuracy caused by multi-parameter identification.This method provides a new estimation strategy for accurately identifying the parameters of the static var compensator model.Estimation results show that the parameter estimation method can be an effective tool to solve the problem of parameter identification for the SVC model.

Multifaceted Insight into Sensitivity Analysis and Environmental Impact on Human Health of Soil Contamination Risk Assessment

Sensitivity analysis is a valuable method for evaluating the impact of model parameters on health risk characterization,thereby supporting the prediction of critical uncertainty factors.However,limitations arise in terms of cross-disciplinary discussions and in-depth analyses of previous research.To overcome these limitations,a systematic and multifaceted approach was introduced for analyzing the parameter sensitivities in soil contamination risk assessment.This approach specifically targeted the 12 main parameters associated with 65 soil contaminants for health risk assessment,employing detailed authoritative statistics for risk assessment.Screening analysis revealed that identified heavy metals and organics were influenced by key parameters,such as PM_(10),body weight of adults(BW_(a)),daily air inhalation rate of adults(DAIR_(a)),air exchange rate(ER),and typical soil parameters.PM_(10) showed a positive 100%correlation with inorganics and metals,but BW_(a) and DAIR_(a) exhibited different impacts on different chemicals,with an increase in potential risk observed with higher BW_(a) and lower DAIR_(a).Furthermore,incorporating soil parameters in the analysis showed that compact soil could improve the protection against vapor organic compounds for human health.This refined study presents a comprehensive strategy for sensitivity analysis in health risk assessment of soil contamination,thereby offering substantial support for the protection and preservation of human health.A logical framework also was provided for addressing the limitations of sensitivity analysis and facilitating an understanding of the complex relationships between model parameters and the health risk of soil contamination.

Sensitivity analysis of relevant parameters in complicated mine ventilation network by numerical test

Depending on the numerical test approach on a computer, the relationships among relevant parameters, eg branch number, node number, mesh number, computation accuracy, preliminary value of airflow rate, iteration number, computation time and convergence in a mine ventilation network analysis, were investigated based on 5 mine ventilation systems. The results show that a higher computation accuracy greatly influences the iteration number. When the accuracy reaches 10-6m3·s-1 for solving a complicated mine ventilation network, the running time is too long though a high-speed computer is used. The preliminary value of airflow rate in the range of 1100m3·s-1 has little effects the iteration number. The structure of network also has some effect on the iteration number.

Sensitivity Analysis of Thermal Equilibrium Parameters of MIKE 11 Model:A Case Study of Wuxikou Reservoir in Jiangxi Province of China

Sensitivity analysis of thermal equilibrium parameters in the reservoir module of MIKE 11 model was conducted for the Wuxikou Reservoir in Jiangxi Province of China in order to apply the module to the environmental impact assessment to accurately predict water temperature of reservoirs.Results showed that radiation parameter A and evaporation-first parameter were much more sensitive than other parameters.The values of the radiation parameter A ranged from 0.10 to 0.34.The values of evaporation-first parameter varied from 0 to 10.The sensitivity of solar absorption parameters was less than that of evaporation parameter,of which light attenuation values ranged from 0.5 to 0.7,and this parameter would not impact model results if it was more than 2.Constants in Beer's law ranged from 0.2 to 0.7.Radiation parameter B was not more sensitive than evaporation parameter and its reasonable range was higher than 0.48.The fitting curves showed consistent changing tendency for these parameters within the reasonable ranges.Additionally,all the thermal equilibrium parameters had much more important effects on surface water temperature than deep water temperature.Moreover,if no observed data could be obtained,the local empirical value would be used to input to the MIKE 11 model to simulate the changes in the discharged outflow-water temperature qualitatively.

Sensitivity analysis of distributed parameter elements in high-speed circuit networks

This paper presents an analysis method, based on MacCormack＇s technique, for the evaluation of the time domain sensitivity of distributed parameter elements in high-speed circuit networks. Sensitivities can be calculated from electrical and physical parameters of the distributed parameter elements. The proposed method is a direct numerical method of time-space discretization and does not require complicated mathematical deductive process. Therefore, it is very convenient to program this method. It can be applied to sensitivity analysis of general transmission lines in linear or nonlinear circuit networks. The proposed method is second-order-accurate. Numerical experiment is presented to demonstrate its accuracy and efficiency.

Analysis on Sensitivity of Power System Stability to Generator Parameters

The sensitivity of power system stability (including transient and dynamic stabilities) to generator parameters (including parameters of generator model, excitation system and power system stabilizer) is analyzed in depth by simulations. From the tables and plots of the resultant simulated data, a number of useful rules are revealed. These rules can be directly applied to the engineering checking of generator parameters. Because the complex theoretical analyses are circumvented, the checking procedure is greatly simplified, remarkably promoting the working efficiency of electrical engineers on site.

Parameter Sensitivity and Qualitative Analysis of Dynamics of Ovarian Tumor Growth Model with Treatment Strategy

In this paper, we are interested to find the most sensitive parameter, local and global stability of ovarian tumor growth model. For sensitivity analysis, we use Latin Hypercube Sampling (LHS) method to generate sample points and Partial Rank Correlation Coefficient (PRCC) method, uses those sample points to find out which parameters are important for the model. Based on our findings, we suggest some treatment strategies. We investigate the sensitivity of the parameters for tumor volume, y, cell nutrient density, Q and maximum tumor size, ymax. We also use Scatter Plot method using LHS samples to show the consistency of the results obtained by using PRCC. Moreover, we discuss the qualitative analysis of ovarian tumor growth model investigating the local and global stability.

Modeling and Sensitivity Analysis of Navigation Parameter Errors for Airborne Synthetic Aperture Radar Stereo Geolocation

为高分辨率的在空中的合成的孔雷达(SAR ) 立体声 geolocation 申请，最后的 geolocation 精确性被各种各样的错误参数来源影响。在这份报纸，一个在空中的 SAR 立体声 geolocation 参数错误模型，包含参数错误在飞行平台上源于航行系统，被提出了。而且，为当模特儿的一种接近直接方法和航行参数错误的敏感分析也被给。这个方法直接使用扎根的参考书为地面目标点计算在参数错误和最终的 geolocation 错误之间的协变性矩阵关系。另外，利用真飞行磁道参数鈥 ? 错误，这份报纸为在空中的 SAR 立体声 geolocation 模型给了方法和相应敏感分析的确认并且证明了它的效率。