Extended Fourier Amplitude Sensitivity Test Research Articles

LSTM Based EFAST Global Sensitivity Analysis for Interwell Connectivity Evaluation Using Injection and Production Fluctuation Data

In petroleum production system, interwell connectivity evaluation is a significant process to understand reservoir properties comprehensively, determine water injection rate scientifically, and enhance oil recovery effectively for oil and gas field. In this paper, a novel long short-term memory (LSTM) neural network based global sensitivity analysis (GSA) method is proposed to analyse injector-producer relationship. LSTM neural network is employed to build up the mapping relationship between production wells and surrounding injection wells using the massive historical injection and production fluctuation data of a synthetic reservoir model. Next, the extended Fourier amplitude sensitivity test (EFAST) based GSA approach is utilized to evaluate interwell connectivity on the basis of the generated LSTM model. Finally, the presented LSTM based EFAST sensitivity analysis method is applied to a benchmark test and a synthetic reservoir model. Experimental results show that the proposed technique is an efficient method for estimating interwell connectivity.

Global and local sensitivity analysis to improve the understanding of physically-based urban wash-off models from high-resolution laboratory experiments

Physically-based urban wash-off models are a promising means of studying the transport of finer suspended solids and their associated pollutants during rain events, considering spatial and temporal heterogeneities. This study contributes to the understanding of these models through an in-depth sensitivity analysis to provide the necessary information to simplify the model and deal with parameter identifiability. First, based on twelve tailored high-resolution experiments, the accurate measurement of input variables was used to study the parameters of the Hairsine-Rose sediment transport model through a global sensitivity analysis. Using Standardized Regression Coefficients (SRC) and Extended Fourier Amplitude Sensitivity Test (EFAST) methods, the analysis showed that both the total washed-off mass and the TSS peaks concentration are highly sensitive to the critical mass, which considers the reduction in the detachment of particles when the sediment available decreases and is scattered over the surface. In addition, the rain- and flow-driven detachment parameters were presented as key for smaller and larger sediment particles, respectively. Then, those uncertainties that are associated in field studies with the determination of the model input variables were also considered by conducting a local sensitivity analysis. The initial load of sediment and the mean grain size were seen to be the most important variables, thus underlining the need for very accurate measurements here. Moreover, a precise definition of Harsine-Rose parameters is also necessary to achieve reliable results in order to work on treatment and management techniques to minimize the impact of urban surface contaminants on urban environments.

An Integrated Yield Prediction Model for Greenhouse Tomato

The commonly used greenhouse crop yield prediction models today have their specific application scenarios, which may not ensure the accuracy of the results if the greenhouse environment changes. This greatly restricts their use in the greenhouse environment. To solve this problem, two widely used tomato growth models were compared in the study: TOMGRO and Vanthoor, and then an integrated model was obtained. Through the extended Fourier amplitude sensitivity test (EFAST), the model parameters were divided into three categories: optimized, fixed and ignored. In addition, Bayesian optimization was used as an optimization algorithm, through which the parameters applicable to the greenhouse can be optimized based on the greenhouse data. Compared with TOMGRO and Vanthoor, the output of the integrated model was more reasonable and universal, and the RMSE in the integrated model was 2.5974 while that in TOMGRO and Vanthoor both were over 17, reflecting the fact that the model output was closer to the actual value. According to the verification results of four-year greenhouse data, the model had high performance in predicting yield.

Estimating Forest Canopy Height Using MODIS BRDF Data Emphasizing Typical-Angle Reflectances

Forest-canopy height is an important parameter for the estimation of forest biomass and terrestrial carbon flux and climate-change research at regional and global scales. Currently, various methods combining Light Detection and Ranging (LiDAR) data with various auxiliary data, particularly satellite remotely sensed reflectances, have been widely used to produce spatially continuous canopy-height products. However, current methods in use for remote sensing reflectances mainly focus on the nadir view direction, while anisotropic reflectances, which are theoretically more sensitive to the forest canopy height in the multiangle remote sensing field, have rarely been explored. Here, we attempted to examine the potential of using modeled multiangle reflectances at three typical viewing angles (i.e., from the hotspot, darkspot, and nadir directions) to estimate forest-canopy height as auxiliary data sources. First, the sensitivities of the typical angular reflectances as a function of forest canopy height were fully examined using the Extended Fourier Amplitude Sensitivity Test (EFAST) method based on the 4-scale Bidirectional Reflectance Distribution Function (BRDF) model simulations. This indicated that reflectances in the off-nadir viewing directions are generally sensitive to canopy-height variations. Then, the canopy heights were extracted from airborne Laser Vegetation Imaging Sensor (LVIS) data, which were further divided into training and validation data. Moderate Resolution Imaging Spectroradiometer (MODIS) multiangle reflectances at typical viewing angles were calculated from the MODIS BRDF parameter product (MCD43A1, version 6) as partial training-input data, based on a hotspot-adjusted, kernel-driven linear BRDF model. Subsequently, the Random Forest (RF) machine learning model was trained to acquire the relationship between the extracted canopy heights and the corresponding MODIS typical viewing reflectances. The trained model was further applied to estimate the canopy height metrics in the study areas of Howland Forest, Harvard Forest, and Bartlett Forest. Finally, the estimated canopy heights were independently validated by canopy heights extracted from the LVIS data. The results indicate that the canopy heights modeled through this method exhibit generally high accordance with the LVIS-derived canopy heights (R = 0.65−0.67; RMSE = 3.63−5.78). The results suggest that the MODIS multiangle reflectance data at typical observation angles contain important information regarding forest canopy height and can, therefore, be used to estimate forest canopy height for various ecological applications.

Dynamic Modeling of Microalgae Growth and Lipid Production under Transient Light and Nitrogen Conditions

We developed a new dynamic model to characterize how light and nitrogen regulate the cellular processes of photosynthetic microalgae leading to transient changes in the production of neutral lipids, carbohydrates, and biomass. Our model recapitulated the versatile neutral lipid synthesis pathways via (i) carbon reuse from carbohydrate metabolism under nitrogen sufficiency and (ii) fixed carbon redirection under nitrogen depletion. We also characterized the effects of light adaptation, light inhibition hysteresis, and nitrogen limitation on photosynthetic carbon fixation. The formulated model was calibrated and validated with experimental data of Dunaliella viridis cultivated in a lab-scale photobioreactor (PBR) under various light (low/moderate/high) and nitrogen (sufficient/limited) conditions. We conducted the identifiability, uncertainty, and sensitivity analyses to verify the model reliability using the profile likelihood method, the Markov chain Monte Carlo (MCMC) technique, and the extended Fourier Amplitude Sensitivity Test (eFAST). Our model predictions agreed well with experimental observations and suggested potential model improvement by incorporating a lipid degradation mechanism. The insights from our model-driven analysis helped improve the mechanistic understanding of transient algae growth and bioproducts formation under environmental variations and could be applied to optimize biofuel and biomass production.

A Comparison Study of Sensitivity on PJ and NPS Models in China Seas

Evaporation duct is an ubiquitous natural phenomenon over the ocean and can be diagnosed by evaporation duct model. The model proposed by Paulus and Jeske and another model established by the American naval postgraduate school are the most widely used. They are called PJ model and NPS model, respectively. Two methods are used to investigate the global sensitivity of PJ model and NPS model in China Seas. The first method is based on meteorological and oceanographic observation data in China Seas. Considering the system random error caused by sensor measurement inaccuracies, the mean relative error and mean absolute error are used as criterion for sensitivity analysis. The second method, called Extended Fourier Amplitude Sensitivity Test (EFAST), takes into account the interaction between input parameters and is used for sensitivity analysis. The results show that NPS model is more sensitive to the random errors of sensors than PJ model. The mean relative errors of PJ model and NPS model are 11.43% and 14.81%, respectively. The results of global sensitivity parameter analysis indicate that wind speed is the key factor of PJ model, while all input parameter of NPS model have relatively large total sensitivity index. In addition, sensitivity analysis results confirm that wind speed is one of main driving factors for the formation of evaporation duct. These results are valuable for the selection of diagnosis models for evaporation duct, the evaluation of radio wave propagation in the marine atmospheric surface layer, and the prediction technique of evaporation duct based on numerical weather prediction (NWP) in China seas.

Predicting leaf chlorophyll content and its nonuniform vertical distribution of summer maize by using a radiation transfer model

Remote sensing technology is an effective method of monitoring chlorophyll content, an important parameter for vegetation health. The chlorophyll information based on spectral information needs to consider the vertical characteristics of plants. Hyperspectral features [spectral reflectance (SR), spectral indices, and wavelet coefficients (WC)] were first selected to construct the cost function in the PROSPECT model-optimized inversion to improve the accuracy and efficiency of leaf chlorophyll content (LCC) inversion. Second, the sensitivity of LCC to leaf SR, vegetation index ( VI ), and WC were analyzed. Finally, LCC was inverted by the PROSPECT model using the iterative inversion algorithm, and the chlorophyll content of the vertical profile in maize was monitored. The following results were obtained. (1) According to the extended Fourier amplitude sensitivity test (EFAST) used to construct the cost-function inversion of LCC, the normalized difference vegetation index canste (NDVIcanste) and WC based on EFAST method which was used to construct the cost-function inversion of LCC, yielded higher accuracy than other spectral features. These two methods, combined with sensitivity analysis can provide accurate inversion results by weakening the influence of other parameters on spectral changes and eliminating the interference information between bands. (2) The cost function based on NDVIcanste in the LCC optimization exhibited overestimation, whereas WC can solve the problem efficiently. The continuous wavelet transform can extract weak information among the spectra, whereas the other two methods of SR and VI cannot easily obtain this information. (3) The vertical distribution of LCC in different maize varieties and treatments is in accordance with the parabola law, but the chlorophyll content of the different leaf positions on the vertical profile is somewhat different. The results reflect the vertical distribution of chlorophyll content through the radiation transfer of leaves, thus providing a theoretical basis for their further combination.

Global sensitivity analysis of wheat grain yield and quality and the related process variables from the DSSAT-CERES model based on the extended Fourier Amplitude Sensitivity Test method

A crop growth model, integrating genotype, environment, and management factor, was developed to serve as an analytical tool to study the influence of these factors on crop growth, production, and agricultural planning. A major challenge of model application is the optimization and calibration of a considerable number of parameters. Sensitivity analysis (SA) has become an effective method to identify the importance of various parameters. In this study, the extended Fourier Amplitude Sensitivity Test (EFAST) approach was used to evaluate the sensitivity of the DSSAT-CERES model output responses of interest to 39 crop genotype parameters and six soil parameters. The outputs for the SA included grain yield and quality (take grain protein content (GPC) as an indicator) at maturity stage, as well as leaf area index, aboveground biomass, and aboveground nitrogen accumulation at the critical process variables. The key results showed that: (1) the influence of parameter bounds on the sensitivity results was slight and less than the impacts from the significance of the parameters themselves; (2) the sensitivity parameters of grain yield and GPC were different, and the sensitivity of the interactions between parameters to GPC was greater than those between the parameters to grain yield; and (3) the sensitivity analyses of some process variables, including leaf area index, aboveground biomass, and aboveground nitrogen accumulation, should be performed differently. Finally, some parameters, which improve the model's structure and the accuracy of the process simulation, should not be ignored when maturity output as an objective variable is studied.

Sensitivity and Uncertainty Analysis of One-Dimensional Tanaka and Liang-Rogers Shape Memory Alloy Constitutive Models.

A shape memory alloy (SMA) can remember its original shape and recover from strain due to loading once it is exposed to heat (shape memory effect). SMAs also exhibit elastic response to applied stress above the characteristic temperature at which transformation to austenite is completed (pseudoelasticity or superelasticity). Shape memory effect and pseudoelasticity of SMAs have been addressed by several microscopic thermodynamic and macroscopic phenomenological models using different modeling approaches. The Tanaka and Liang-Rogers models are two of the most widely used macroscopic phenomenological constitutive models for describing SMA behavior. In this paper, we performed sensitivity and uncertainty analysis using Sobol and extended Fourier Amplitude Sensitivity Testing (eFAST) methods for the Tanaka and Liang-Rogers models at different operating temperatures and loading conditions. The stress-dependent and average sensitivity indices have been analyzed and are presented for determining the most influential parameters for these models. The results show that variability is primarily caused by a change in operating temperature and loading conditions. Both models appear to be influenced by the uncertainty in elastic modulus of the material significantly. The analyses presented in this paper aim to provide a better insight for designing applications using SMAs by increasing the understanding of these models’ sensitivity to the input parameters and the cause of output variability due to uncertainty in the same input parameters.

Practical Experience of Sensitivity Analysis: Comparing Six Methods, on Three Hydrological Models, with Three Performance Criteria

Currently, practically no modeling study is expected to be carried out without some form of Sensitivity Analysis (SA). At the same time, there is a large number of various methods and it is not always easy for practitioners to choose one. The aim of this paper is to briefly review main classes of SA methods, and to present the results of the practical comparative analysis of applying them. Six different global SA methods: Sobol, eFAST (extended Fourier Amplitude Sensitivity Test), Morris, LH-OAT, RSA (Regionalized Sensitivity Analysis), and PAWN are tested on three conceptual rainfall-runoff models with varying complexity: (GR4J, Hymod, and HBV) applied to the case study of Bagmati basin (Nepal). The methods are compared with respect to effectiveness, efficiency, and convergence. A practical framework of selecting and using the SA methods is presented. The result shows that, first of all, all the six SA methods are effective. Morris and LH-OAT methods are the most efficient methods in computing SI and ranking. eFAST performs better than Sobol, and thus it can be seen as its viable alternative for Sobol. PAWN and RSA methods have issues of instability, which we think are due to the ways Cumulative Distribution Functions (CDFs) are built, and using Kolmogorov–Smirnov statistics to compute Sensitivity Indices. All the methods require sufficient number of runs to reach convergence. Difference in efficiency of different methods is an inevitable consequence of the differences in the underlying principles. For SA of hydrological models, it is recommended to apply the presented practical framework assuming the use of several methods, and to explicitly take into account the constraints of effectiveness, efficiency (including convergence), ease of use, and availability of software.

Probabilistic assessment of the impact of bottom sediment on doses to humans from a groundwater-mediated radionuclide release in a farm-lake scenario

Radionuclide transport with groundwater flow and subsequent doses to people are an aspect to be studied when assessing the long-term safety of geological nuclear waste repositories. A scenario where the radionuclide release migrates through a three-layer sediment structure of a lake in a farming environment is presented in this paper. The sediment column consists of deep (till), intermediate (glacio-aquatic sediment) and top layers (clay). The radionuclide release is assumed to enter the deep sediment layer from a bedrock fracture system at a rate of 1 Bq yr−1. The main objectives of the paper are to investigate the most contributing parameters, especially linked to the sediment layers, to the overall dose estimates for humans. The sensitivity analysis was conducted in two phases where the Morris method was used for screening and the Extended Fourier Amplitude Sensitivity Testing and Sobol’s methods were used for estimating total-order indices. The studied radionuclides, 36Cl, 135Cs, 129I, 94Nb, 237Np, 90Sr, 99Tc and 238U, exhibit differences in how the sediment layers affect the concentration in the lake water used for drinking, irrigation and watering cattle and subsequently the dose conversion factors for humans through ingestion, inhalation and external radiation.

Evaluating the effects of limited irrigation on crop water productivity and reducing deep groundwater exploitation in the North China Plain using an agro-hydrological model: I. Parameter sensitivity analysis, calibration and model validation

The agro-hydrological Soil-Water-Atmosphere-Plant-WOrld-FOod-STudy (SWAP-WOFOST) model in a distributed manner represents an important tool for evaluating agro-hydrological cycles and irrigation strategies at different spatiotemporal scales. The reliability of the model simulations and evaluations is dependent on the generation of the distributed simulation units that account for the spatial heterogeneity of various factors, as well as parameter calibration and model validation. In this study, we focused on the most typical overexploited deep groundwater area in the North China Plain (NCP). First, the extended Fourier amplitude sensitivity test (EFAST) was used to conduct global sensitivity analyses for three modules in the SWAP-WOFOST model to identify the parameters that significantly influence the objective variables for calibration at the six experimental stations in the study area. On this basis, the parameters were calibrated and validated in detail using abundant observed data from each station. The normalized root mean square error (NRMSE) values for soil water content, soil salt concentration, winter wheat leaf area index (LAI), winter wheat aboveground biomass, winter wheat yield, summer maize LAI, summer maize aboveground biomass and summer maize yield were 14.93%, 27.20%, 24.60%, 25.27%, 23.12%, 24.55%, 21.33% and 17.94%, respectively, during the calibration period; and the corresponding NRMSE values were 16.26%, 29.36%, 24.20%, 22.75%, 21.77%, 22.03%, 24.38% and 18.62%, respectively, during the validation period. The model provided a good simulation for the soil water contents and summer maize yields and a fair simulation for the other objective variables. Furthermore, a distributed SWAP-WOFOST model was generated by overlaying 12 maps involving meteorology, soil, crops, land use, water resources and administrative divisions, yielding 2809 simulation units. Finally, the simulation accuracy of the distributed model was evaluated under the current irrigation conditions. The results showed that the simulated yields of winter wheat and summer maize were consistent with the statistical values, and the simulated evapotranspiration matched the remote sensing data with acceptable precision. In summary, the distributed SWAP-WOFOST model could be used as an effective tool for simulating crop water productivity in time and space under limited irrigation scenarios and for evaluating the effect of optimized limited irrigation schemes on reducing deep groundwater exploitation in this region.

Parameter Optimization of a Discrete Scattering Model by Integration of Global Sensitivity Analysis Using SMAP Active and Passive Observations

Active and passive microwave signatures respond differently to the land surface and provide complementary information on the characteristics of the observed scenes. The objective of this paper is to explore the synergy of active radar and passive radiometer observations at the same spatial scale to constrain a discrete radiative transfer model, the Tor Vergata (TVG) model, to gain insights into the microwave scattering and emission mechanisms over grasslands. The TVG model can simultaneously simulate the backscattering coefficient and emissivity with a set of input parameters. To calibrate this model, in situ soil moisture and temperature data collected from the Maqu area in the northeastern region of the Tibetan Plateau, interpolated leaf area index (LA!) data from the Moderate Resolution Imaging Spectroradiometer LAI eight-day products, and concurrent and coincident Soil Moisture Active Passive (SMAP) radar and radiometer observations are used. Because this model needs numerous input parameters to be driven, the extended Fourier amplitude sensitivity test is first applied to conduct global sensitivity analysis (GSA) to select the sensitive and insensitive parameters. Only the most sensitive parameters are defined as free variables, to separately calibrate the activeonly model (TVG-A), the passive-only model (TVG-P), and the active and passive combined model (TVG-AP). The accuracy of the calibrated models is evaluated by comparing the SMAP observations and the model simulations. The results show that TVG-AP can well reproduce the backscattering coefficient and brightness temperature, with correlation coefficients of 0.87, 0.89, 0.78, and 0.43 and root-mean-square errors of 0.49 dB, 0.52 dB, 7.20 K, and 10.47 K for σ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">HH</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sup> , σ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">VV</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sup> , T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">BH</sub> , and T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">BV</sub> , respectively. In contrast, TVG-A and TVG-P can only accurately model the backscattering coefficient and brightness temperature, respectively. Without any modifications of the calibrated parameters, the error metrics computed from the validation data are slightly worse than those of the calibration data. These results demonstrate the feasibility of the synergistic use of SMAP active radar and passive radiometer observations under the unified framework of a physical model. In addition, the results demonstrate the necessity and effectiveness of applying GSA in model optimization. It is expected that these findings can contribute to the development of model-based soil moisture retrieval methods using active and passive microwave remote sensing data.

Uncertainty Study and Parameter Optimization of Carbon Footprint Analysis for Fermentation Cylinder

With the rapid development of industry, problems for the ecological environment are increasing day by day, among which carbon pollution is particularly serious. Product carbon emission accounting is the core of sustainable green design. In this paper, the beer fermentation cylinder is taken as an example for low carbon design to get the best combination of design parameters when the carbon emission is the smallest. The life cycle assessment method is used to calculate the carbon footprint of products. In order to analyse the uncertainty and sensitivity of the method, an uncertainty analysis method using data quality characteristics as input of Monte Carlo is proposed. Sensitivity analysis is carried out by multivariate statistical regression and Extended Fourier Amplitude Sensitivity Test (EFAST). The system boundary of fermentation cylinder is determined and the carbon emissions of life cycle are calculated. The quality characteristics of life cycle inventory data (LCI) data are analysed and Monte Carlo simulation is carried out to quantify the uncertainty of LCI. EFAST is used to calculate the sensitivity of LCI and the results are compared with those of multivariate statistical regression to verify the feasibility of the method. Finally, response surface methodology (RSM) is used to optimize the design of parameters. It provides guidance for the establishment of product carbon emission model and low carbon design.

Theoretical Study of Global Sensitivity Analysis of L-Band Radar Bistatic Scattering for Soil Moisture Retrieval

This letter explores the optimal bistatic radar configurations for bare soil moisture retrieval at L-band using a global sensitivity analysis method, the extended Fourier amplitude sensitivity test (EFAST) algorithm. Complete sets of bistatic scattering, covering a wide range of geometric parameters and ground surface conditions, are simulated by the well-established advanced integral equation model. The sensitivity of radar bistatic signals to soil moisture and surface roughness, and the interactions among the parameters are quantified using the EFAST algorithm. The results show that in bistatic scattering, VV polarization has notably higher sensitivity to soil moisture than HH polarization, particularly at large incident angles. For VV polarization, as incident angle increases, the sensitivity zone of soil moisture expands and shifts toward the forward direction, specifically at small azimuth scattering angles and large scattering angles, thereby becoming promising configurations for soil moisture retrieval. For HH polarization, in contrast, the sensitive zone gradually moves to the backward direction as incident angle increases, and an intermediate incident angle (e.g., 40°) is recommended for retrieving soil moisture by considering both sensitivity strength and parameter interaction effects.

Global sensitivity analysis of the APSIM-Oryza rice growth model under different environmental conditions

This study conducted the global sensitivity analysis of the APSIM-Oryza rice growth model under eight climate conditions and two CO2 levels using the extended Fourier Amplitude Sensitivity Test method. Two output variables (i.e. total aboveground dry matter WAGT and dry weight of storage organs WSO) and twenty parameters were analyzed. The ±30% and ±50% perturbations of base values were used as the ranges of parameter variation, and local fertilization and irrigation managements were considered. Results showed that the influential parameters were the same under different environmental conditions, but their orders were often different. Climate conditions had obvious influence on the sensitivity index of several parameters (e.g. RGRLMX, WGRMX and SPGF). In particular, the sensitivity index of RGRLMX was larger under cold climate than under warm climate. Differences also exist for parameter sensitivity of early and late rice in the same site. The CO2 concentration did not have much influence on the results of sensitivity analysis. The range of parameter variation affected the stability of sensitivity analysis results, but the main conclusions were consistent between the results obtained from the ±30% perturbation and those obtained the ±50% perturbation in this study. Compared with existing studies, our study performed the sensitivity analysis of APSIM-Oryza under more environmental conditions, thereby providing more comprehensive insights into the model and its parameters.

Fuzzy Sensitivity Analysis in the Context of Dimensional Management

Real components always deviate from their ideal dimensions. This makes every component, even a serial production, unique. Although they look the same, differences can always be observed due to different scattering factors and variations in the manufacturing process. All these factors inevitably lead to parts that deviate from their ideal shape and, therefore, have different properties than the ideal component. Changing properties can lead to major problems or even failure during operation. It is necessary to specify the permitted deviations to ensure that every single product nevertheless meets its technical requirements. Furthermore, it is necessary to estimate the consequences of the permitted deviations, which is done via tolerance analysis. During this process, components are assembled virtually and varied with the uncertainties specified by the tolerances. A variation simulation is one opportunity to calculate these effects for geometric deviations. Since tolerance analysis enables engineers to identify weak points in an early design stage, it is important to know the contribution that every single tolerance has on a certain quality-relevant characteristic, to restrict or increase the correct tolerances. In this paper, a fuzzy-based method to calculate the sensitivity is introduced and compared with the commonly used extended Fourier amplitude sensitivity test (EFAST) method. Special focus of this work is the differentiation of the sensitivity for the total system and the sensitivities for the subsystems defined by the α-cuts of the fuzzy numbers. It discusses the impact of the number of evaluations and nonlinearity on sensitivity for EFAST and the fuzzy-based method.

Fast sensitivity analysis methods for computationally expensive models with multi-dimensional output

Abstract. Global sensitivity analysis (GSA) is a powerful approach in identifying which inputs or parameters most affect a model's output. This determines which inputs to include when performing model calibration or uncertainty analysis. GSA allows quantification of the sensitivity index (SI) of a particular input – the percentage of the total variability in the output attributed to the changes in that input – by averaging over the other inputs rather than fixing them at specific values. Traditional methods of computing the SIs using the Sobol and extended Fourier Amplitude Sensitivity Test (eFAST) methods involve running a model thousands of times, but this may not be feasible for computationally expensive Earth system models. GSA methods that use a statistical emulator in place of the expensive model are popular, as they require far fewer model runs. We performed an eight-input GSA, using the Sobol and eFAST methods, on two computationally expensive atmospheric chemical transport models using emulators that were trained with 80 runs of the models. We considered two methods to further reduce the computational cost of GSA: (1) a dimension reduction approach and (2) an emulator-free approach. When the output of a model is multi-dimensional, it is common practice to build a separate emulator for each dimension of the output space. Here, we used principal component analysis (PCA) to reduce the output dimension, built an emulator for each of the transformed outputs, and then computed SIs of the reconstructed output using the Sobol method. We considered the global distribution of the annual column mean lifetime of atmospheric methane, which requires ∼ 2000 emulators without PCA but only 5–40 emulators with PCA. We also applied an emulator-free method using a generalised additive model (GAM) to estimate the SIs using only the training runs. Compared to the emulator-only methods, the emulator–PCA and GAM methods accurately estimated the SIs of the ∼ 2000 methane lifetime outputs but were on average 24 and 37 times faster, respectively.

Parameter sensitivity analysis of the AquaCrop model based on extended fourier amplitude sensitivity under different agro-meteorological conditions and application

Sensitivity analysis (SA) can be used to identify the effects of crop model input parameters on model results. Previous studies have indicated that the ranges, distributions, and properties of many parameters are difficult to estimate, though some may be acquired indirectly from literature. Parameter ranges are often adjusted to fit specific applications, but some are not representative of crop properties. The objectives of this study were to: (i) comprehensively quantify the effects of parameter variation on the sensitivity of AquaCrop output variables based on the extended Fourier amplitude sensitivity test, (ii) study the effects of parameter variation on the sensitivity of output variables over time, and (iii) calibrate and simplify the AquaCrop model based on the SA results under different agro-meteorological conditions. The results demonstrated that output variable sensitivity varied in response to crop parameter variation. The first order sensitivity index (FOSI) demonstrated that some crop parameters were sensitive to yield and maximum dry biomass. The results from the time-dependent FOSI analysis revealed that some parameters were insensitive to yield and maximum dry biomass but were sensitive to canopy cover and dry biomass during certain wheat growth stages. The total sensitivity index (TSI) and time-dependent TSI of crop parameters were more sensitive than the FOSI and time-dependent FOSI of crop parameters. The sensitivities of winter and spring wheat simulations based on FOSI and time-dependent FOSI were consistent; however, some differences existed between simulations based on TSI and time-dependent TSI. Simulations based on SA were more accurate than previously reported results. Results from the calibrated and simplified AquaCrop model revealed good consistency between simulated and measured canopy cover, biomass, and yield. Future studies should focus on analyzing the sensitivity of crop parameters to dynamic output variables over time to better calibrate and simplify the AquaCrop model.

Integrating Extended Fourier Amplitude Sensitivity Test and Set Pair Analysis for Sustainable Development Evaluation from the View of Uncertainty Analysis

It is of importance but great difficulty to objectively and quantitatively evaluate the sustainable development level, especially in the weight determination process and uncertainty evaluation. The traditional weight determination methods hardly reflect the coupling effect (interaction) among the indices. More importantly, conventional evaluation methods seldom consider the uncertainties of the indices in the index system. Thus, it is indispensable to apply a more comprehensive approach to solve these defects. This paper presents a new method to evaluate the sustainable development level. The approach integrates the advantages of the Extended Fourier Amplitude Sensitivity Test (EFAST) and Set Pair Analysis (SPA) (called EFAST-SPA). The EFAST algorithm is used to determine the indices’ weight, and the SPA is employed to handle the uncertain relations in the evaluation system and to calculate the sustainable development level. A quantitative evaluation on the agricultural sustainable development in the middle reaches of Heihe river has been conducted using the EFAST-SPA method. The results have been compared with the traditional entropy method and it was concluded that EFAST-SPA and entropy are highly in line with the actual development status. In most cases, the EFAST-SPA method can describe the development levels more accurately, which reflects a higher reliability and application value of this proposed approach. Moreover, the presented method deepens the understanding of sustainable development evaluation from the view of uncertainty analysis inside the evaluation system.