Uncertainty and disturbance estimator-based model predictive control for wet flue gas desulphurization system

Wet flue gas desulphurization technology is widely used in the industrial process for its capability of efficient pollution removal.The desulphurization control system,however,is subjected to complex reaction mechanisms and severe disturbances,which make for it difficult to achieve certain practically relevant control goals including emission and economic performances as well as system robustness.To address these challenges,a new robust control scheme based on uncertainty and disturbance estimator(UDE)and model predictive control(MPC)is proposed in this paper.The UDE is used to estimate and dynamically compensate acting disturbances,whereas MPC is deployed for optimal feedback regulation of the resultant dynamics.By viewing the system nonlinearities and unknown dynamics as disturbances,the proposed control framework allows to locally treat the considered nonlinear plant as a linear one.The obtained simulation results confirm that the utilization of UDE makes the tracking error negligibly small,even in the presence of unmodeled dynamics.In the conducted comparison study,the introduced control scheme outperforms both the standard MPC and PID(proportional-integral-derivative)control strategies in terms of transient performance and robustness.Furthermore,the results reveal that a lowpass-filter time constant has a significant effect on the robustness and the convergence range of the tracking error.

Acoustic propagation uncertainty in internal wave environments using an ocean-acoustic joint model

An ocean-acoustic joint model is developed for research of acoustic propagation uncertainty in internal wave environments.The internal waves are numerically produced by tidal forcing over a continental slope using an ocean model.Three parameters(i.e.,internal wave,source depth,and water depth)contribute to the dynamic waveguide environments,and result in stochastic sound fields.The sensitivity of the transmission loss(TL)to environment parameters,statistical characteristics of the TL variation,and the associated physical mechanisms are investigated by the Sobol sensitivity analysis method,the Monte Carlo sampling,and the coupled normal mode theory,respectively.The results show that the TL is most sensitive to the source depth in the near field,resulted from the initial amplitudes of higher-order modes;while in middle and far fields,the internal waves are responsible for more than 80%of the total acoustic propagation contribution.In addition,the standard deviation of the TL in the near field and the shallow layer is smaller than those in the middle and far fields and the deep layer.

Spatial Inhomogeneity of Atmospheric CO_(2) Concentration and Its Uncertainty in CMIP6 Earth System Models

This paper provides a systematic evaluation of the ability of 12 Earth System Models(ESMs)participating in the Coupled Model Intercomparison Project Phase 6(CMIP6)to simulate the spatial inhomogeneity of the atmospheric carbon dioxide(CO_(2))concentration.The multi-model ensemble mean(MME)can reasonably simulate the increasing trend of CO_(2) concentration from 1850 to 2014,compared with the observation data from the Scripps CO_(2) Program and CMIP6 prescribed data,and improves upon the CMIP5 MME CO_(2) concentration(which is overestimated after 1950).The growth rate of CO_(2) concentration in the northern hemisphere(NH)is higher than that in the southern hemisphere(SH),with the highest growth rate in the mid-latitudes of the NH.The MME can also reasonably simulate the seasonal amplitude of CO_(2) concentration,which is larger in the NH than in the SH and grows in amplitude after the 1950s(especially in the NH).Although the results of the MME are reasonable,there is a large spread among ESMs,and the difference between the ESMs increases with time.The MME results show that regions with relatively large CO_(2) concentrations(such as northern Russia,eastern China,Southeast Asia,the eastern United States,northern South America,and southern Africa)have greater seasonal variability and also exhibit a larger inter-model spread.Compared with CMIP5,the CMIP6 MME simulates an average spatial distribution of CO_(2) concentration that is much closer to the site observations,but the CMIP6-inter-model spread is larger.The inter-model differences of the annual means and seasonal cycles of atmospheric CO_(2) concentration are both attributed to the differences in natural sources and sinks of CO_(2) between the simulations.

Bayesian partial pooling to reduce uncertainty in overcoring rock stress estimation

The state of in situ stress is a crucial parameter in subsurface engineering,especially for critical projects like nuclear waste repository.As one of the two ISRM suggested methods,the overcoring(OC)method is widely used to estimate the full stress tensors in rocks by independent regression analysis of the data from each OC test.However,such customary independent analysis of individual OC tests,known as no pooling,is liable to yield unreliable test-specific stress estimates due to various uncertainty sources involved in the OC method.To address this problem,a practical and no-cost solution is considered by incorporating into OC data analysis additional information implied within adjacent OC tests,which are usually available in OC measurement campaigns.Hence,this paper presents a Bayesian partial pooling(hierarchical)model for combined analysis of adjacent OC tests.We performed five case studies using OC test data made at a nuclear waste repository research site of Sweden.The results demonstrate that partial pooling of adjacent OC tests indeed allows borrowing of information across adjacent tests,and yields improved stress tensor estimates with reduced uncertainties simultaneously for all individual tests than they are independently analysed as no pooling,particularly for those unreliable no pooling stress estimates.A further model comparison shows that the partial pooling model also gives better predictive performance,and thus confirms that the information borrowed across adjacent OC tests is relevant and effective.

Visualization of uncertainty associated with spatial prediction of continuous variables using HSI color model:a case study of prediction of pH for topsoil in peri-urban Beijing,China

Hue-Saturation-Intensity （HSI） color model, a psychologically appealing color model, was employed to visualize uncertainty represented by relative prediction error based on the case of spatial prediction of pH of topsoil in the peri-urban Beijing. A two-dimensional legend was designed to accompany the visualization-vertical axis （hues） for visualizing the predicted values and horizontal axis （whiteness） for visualizing the prediction error. Moreover, different ways of visualizing uncertainty were briefly reviewed in this paper. This case study indicated that visualization of both predictions and prediction uncertainty offered a possibility to enhance visual exploration of the data uncertainty and to compare different prediction methods or predictions of totally different variables. The whitish region of the visualization map can be simply interpreted as unsatisfactory prediction results, where may need additional samples or more suitable prediction models for a better prediction results.

Robust design of sliding mode control for airship trajectory tracking with uncertainty and disturbance estimation

The robotic airship can provide a promising aerostatic platform for many potential applications.These applications require a precise autonomous trajectory tracking control for airship.Airship has a nonlinear and uncertain dynamics.It is prone to wind disturbances that offer a challenge for a trajectory tracking control design.This paper addresses the airship trajectory tracking problem having time varying reference path.A lumped parameter estimation approach under model uncertainties and wind disturbances is opted against distributed parameters.It uses extended Kalman filter(EKF)for uncertainty and disturbance estimation.The estimated parameters are used by sliding mode controller(SMC)for ultimate control of airship trajectory tracking.This comprehensive algorithm,EKF based SMC(ESMC),is used as a robust solution to track airship trajectory.The proposed estimator provides the estimates of wind disturbances as well as model uncertainty due to the mass matrix variations and aerodynamic model inaccuracies.The stability and convergence of the proposed method are investigated using the Lyapunov stability analysis.The simulation results show that the proposed method efficiently tracks the desired trajectory.The method solves the stability,convergence,and chattering problem of SMC under model uncertainties and wind disturbances.

Framework system and research flow of uncertainty in 3D geological structure models

Uncertainty in 3D geological structure models has become a bottleneck that restricts the development and application of 3D geological modeling.In order to solve this problem during periods of accuracy assessment,error detection and dynamic correction in 3D geological structure models,we have reviewed the current situation and development trends in 3D geological modeling.The main context of uncertainty in 3D geological structure models is discussed.Major research issues and a general framework system of uncertainty in 3D geological structure models are proposed.We have described in detail the integration of development practices of 3D geological modeling systems,as well as the implementation process for uncertainty evaluation in 3D geological structure models.This study has laid the basis to build theoretical and methodological systems for accuracy assessment and error correction in 3D geological models and can assist in improving 3D modeling techniques under complex geological conditions.

Representing Model Uncertainty by Multi-Stochastic Physics Approaches in the GRAPES Ensemble

To represent model uncertainties more comprehensively,a stochastically perturbed parameterization(SPP)scheme consisting of temporally and spatially varying perturbations of 18 parameters in the microphysics,convection,boundary layer,and surface layer parameterization schemes,as well as the stochastically perturbed parameterization tendencies(SPPT)scheme,and the stochastic kinetic energy backscatter(SKEB)scheme,is applied in the Global and Regional Assimilation and Prediction Enhanced System-Regional Ensemble Prediction System(GRAPES-REPS)to evaluate and compare the general performance of various combinations of multiple stochastic physics schemes.Six experiments are performed for a summer month(1-30 June 2015)over China and multiple verification metrics are used.The results show that:(1)All stochastic experiments outperform the control(CTL)experiment,and all combinations of stochastic parameterization schemes perform better than the single SPP scheme,indicating that stochastic methods can effectively improve the forecast skill,and combinations of multiple stochastic parameterization schemes can better represent model uncertainties;(2)The combination of all three stochastic physics schemes(SPP,SPPT,and SKEB)outperforms any other combination of two schemes in precipitation forecasting and surface and upper-air verification to better represent the model uncertainties and improve the forecast skill;(3)Combining SKEB with SPP and/or SPPT results in a notable increase in the spread and reduction in outliers for the upper-air wind speed.SKEB directly perturbs the wind field and therefore its addition will greatly impact the upper-air wind-speed fields,and it contributes most to the improvement in spread and outliers for wind;(4)The introduction of SPP has a positive added value,and does not lead to large changes in the evolution of the kinetic energy(KE)spectrum at any wavelength;(5)The introduction of SPPT and SKEB would cause a 5%-10%and 30%-80%change in the KE of mesoscale systems,and all three stochastic schemes(SPP,SPPT,and SKEB)mainly affect the KE of mesoscale systems.This study indicates the potential of combining multiple stochastic physics schemes and lays a foundation for the future development and design of regional and global ensembles.

Possible Sources of Forecast Errors Generated by the Global/Regional Assimilation and Prediction System for Landfalling Tropical Cyclones. Part Ⅱ: Model Uncertainty

This paper investigates the possible sources of errors associated with tropical cyclone(TC) tracks forecasted using the Global/Regional Assimilation and Prediction System(GRAPES). In Part I, it is shown that the model error of GRAPES may be the main cause of poor forecasts of landfalling TCs. Thus, a further examination of the model error is the focus of Part II.Considering model error as a type of forcing, the model error can be represented by the combination of good forecasts and bad forecasts. Results show that there are systematic model errors. The model error of the geopotential height component has periodic features, with a period of 24 h and a global pattern of wavenumber 2 from west to east located between 60?S and 60?N. This periodic model error presents similar features as the atmospheric semidiurnal tide, which reflect signals from tropical diabatic heating, indicating that the parameter errors related to the tropical diabatic heating may be the source of the periodic model error. The above model errors are subtracted from the forecast equation and a series of new forecasts are made. The average forecasting capability using the rectified model is improved compared to simply improving the initial conditions of the original GRAPES model. This confirms the strong impact of the periodic model error on landfalling TC track forecasts. Besides, if the model error used to rectify the model is obtained from an examination of additional TCs, the forecasting capabilities of the corresponding rectified model will be improved.

Assimilation of temporal-spatial leaf area index into the CERES-Wheat model with ensemble Kalman filter and uncertainty assessment for improving winter wheat yield estimation

To accurately estimate winter wheat yields and analyze the uncertainty in crop model data assimilations, winter wheat yield estimates were obtained by assimilating measured or remotely sensed leaf area index （LAI） values. The performances of the calibrated crop environment resource synthesis for wheat （CERES-Wheat） model for two different assimilation scenarios were compared by employing ensemble Kalman filter （EnKF）-based strategies. The uncertainty factors of the crop model data assimilation was analyzed by considering the observation errors, assimilation stages and temporal-spatial scales. Overalll the results indicated a better yield estimate performance when the EnKF-based strategy was used to comprehen- sively consider several factors in the initial conditions and observations. When using this strategy, an adjusted coefficients of determination （R2） of 0.84, a root mean square error （RMSE） of 323 kg ha-1, and a relative errors （RE） of 4.15% were obtained at the field plot scale and an R2 of 0.81, an RMSE of 362 kg ha-1, and an RE of 4.52% were obtained at the pixel scale of 30 mx30 m. With increasing observation errors, the accuracy of the yield estimates obviously decreased, but an acceptable estimate was observed when the observation errors were within 20%. Winter wheat yield estimates could be improved significantly by assimilating observations from the middle to the end of the crop growing seasons. With decreasing assimilation frequency and pixel resolution, the accuracy of the crop yield estimates decreased; however, the computation time decreased. It is important to consider reasonable temporal-spatial scales and assimilation stages to obtain tradeoffs between accuracy and computation time, especially in operational systems used for regional crop yield estimates.

Identification of the Mechanical Joint Parameters with Model Uncertainty

Joint parameter identification is a key problem in the modeling of complex structures. The behavior of joint may be random due to the random properties of preload and joint geometries, contact surface and its finish, etc. A method is presented to simulate the joint parameters as probabilistic variables. In this method the response surface based model updating method and probabilistic approaches are employed to identify the parameters. The study implies that joint parameters of some structures have normal or nearly normal distributions, and a linear FE model with probabilistic variables could illustrate dynamic characteristics of joints.

A New Tuning Method for Two-Degree-of-Freedom Internal Model Control under Parametric Uncertainty

Internal model control （IMC） yields very good performance for set point tracking, but gives sluggish response for disturbance rejection problem. A two-degree-of-freedom IMC （2DOF-IMC） has been developed to overcome the weakness. However, the setting of parameter becomes a complicated matter if there is an uncertainty model. The present study proposes a new tuning method for the controller. The proposed tuning method consists of three steps. Firstly, the worst case of the model uncertainty is determined. Secondly, the parameter of set point con- troller using maximum peak （Mp） criteria is specified, and finally, the parameter of the disturbance rejection con- troller using gain margin （GM） criteria is obtained. The proposed method is denoted as Mp-GM tuning method. The effectiveness of Mp-GM tuning method has evaluated and compared with IMC-controller tuning program （IMCTUNE） as bench mark. The evaluation and comparison have been done through the simulation on a number of first order plus dead time （FOPDT） and higher order processes. The FOPDT process tested includes processes with controllability ratio in the range 0.7 to 2.5. The higher processes include second order with underdarnped and third order with nonminimum phase processes. Although the two of higher order processes are considered as difficult processes, the proposed Mp-GM tuning method are able to obtain the good controller parameter even under process uncertainties.

Incorporating conceptual and interpretation uncertainty to mineral prospectivity modelling

Prospectivity analyses are used to reduce the exploration search space for locating areas prospective for mineral deposits.The scale of a study and the type of mineral system associated with the deposit control the evidence layers used as proxies that represent critical ore genesis processes.In particular,knowledge-driven approaches(fuzzy logic)use a conceptual mineral systems model from which data proxies represent the critical components.These typically vary based on the scale of study and the type of mineral system being predicted.Prospectivity analyses utilising interpreted data to represent proxies for a mineral system model inherit the subjectivity of the interpretations and the uncertainties of the evidence layers used in the model.In the case study presented,the prospectivity for remobilised nickel sulphide(NiS)in the west Kimberley,Western Australia,is assessed with two novel techniques that objectively grade interpretations and accommodate alternative mineralisation scenarios.Exploration targets are then identified and supplied with a robustness assessment that reflects the variability of prospectivity value for each location when all models are considered.The first technique grades the strength of structural interpretations on an individual line-segment basis.Gradings are obtained from an objective measure of feature evidence,which is the quantification of specific patterns in geophysical data that are considered to reveal underlying structure.Individual structures are weighted in the prospectivity model with grading values correlated to their feature evidence.This technique allows interpreted features to contribute prospectivity proportional to their strength in feature evidence and indicates the level of associated stochastic uncertainty.The second technique aims to embrace the systemic uncertainty of modelling complex mineral systems.In this approach,multiple prospectivity maps are each generated with different combinations of confidence values applied to evidence layers to represent the diversity of processes potentially leading to ore deposition.With a suite of prospectivity maps,the most robust exploration targets are the locations with the highest prospectivity values showing the smallest range amongst the model suite.This new technique offers an approach that reveals to the modeller a range of alternative mineralisation scenarios while employing a sensible mineral systems model,robust modelling of prospectivity and significantly reducing the exploration search space for Ni.

Optimal Parameter and Uncertainty Estimation of a Land Surface Model: Sensitivity to Parameter Ranges and Model Complexities

Most previous land-surface model calibration studies have defined globalranges for their parameters to search for optimal parameter sets. Little work has been conducted tostudy the impacts of realistic versus global ranges as well as model complexities on the calibrationand uncertainty estimates. The primary purpose of this paper is to investigate these impacts byemploying Bayesian Stochastic Inversion (BSI) to the Chameleon Surface Model (CHASM). The CHASM wasdesigned to explore the general aspects of land-surface energy balance representation within acommon modeling framework that can be run from a simple energy balance formulation to a complexmosaic type structure. The BSI is an uncertainty estimation technique based on Bayes theorem,importance sampling, and very fast simulated annealing. The model forcing data and surface flux datawere collected at seven sites representing a wide range of climate and vegetation conditions. Foreach site, four experiments were performed with simple and complex CHASM formulations as well asrealistic and global parameter ranges. Twenty eight experiments were conducted and 50 000 parametersets were used for each run. The results show that the use of global and realistic ranges givessimilar simulations for both modes for most sites, but the global ranges tend to produce someunreasonable optimal parameter values. Comparison of simple and complex modes shows that the simplemode has more parameters with unreasonable optimal values. Use of parameter ranges and modelcomplexities have significant impacts on frequency distribution of parameters, marginal posteriorprobability density functions, and estimates of uncertainty of simulated sensible and latent heatfluxes. Comparison between model complexity and parameter ranges shows that the former has moresignificant impacts on parameter and uncertainty estimations.

Application of SWAT Model to the Olifants Basin: Calibration, Validation and Uncertainty Analysis

The application of the Soil and Water Assessment Tool (SWAT) to the Olifants Basin in South Africa was the focus of our study with emphasis on calibration, validation and uncertainty analysis. The Basin was discretized into 23 sub-basins and 226 Hydrologic Response Units (HRUs) using 3 arc second (90 m × 90 m) pixel resolution SRTM DEM with stream gauge B7H015 as the Basin outlet. Observed stream flow data at B7H015 were used for model calibration (1988-2001) and validation (2002-2013) using the split sample approach. Relative global sensitivity analysis using SUFI-2 algorithm was used to determine sensitive parameters to stream flow for calibration of the model. Performance efficiency of the Olifants SWAT model was assessed using Nash-Sutcliffe (NSE), coefficient of determination (R2), Percent Bias (PBIAS) and Root Mean Square Error-Observation Standard deviation Ratio (RSR). Sensitivity analysis revealed in decreasing order of significance, runoff curve number (CN2), alpha bank factor (ALPHA_BNK), soil evaporation compensation factor (ESCO), soil available water capacity (SOIL_AWC, mm H2O/mm soil), groundwater delay (GW_ DELAY, days) and groundwater “revap” coefficient (GW_REVAP) to be the most sensitive parameters to stream flow. Analysis of the model during the calibration period gave the following statistics;NSE = 0.88;R2 = 0.89;PBIAS = -11.49%;RSR = 0.34. On the other hand, statistics during the validation period were NSE = 0.67;R2 = 0.79;PBIAS = -20.69%;RSR = 0.57. The observed statistics indicate the applicability of the SWAT model in simulating the hydrology of the Olifants Basin and therefore can be used as a Decision Support Tool (DST) by water managers and other relevant decisions making bodies to influence policy directions on the management of watershed processes especially water resources.

Uncertainty of Slope Length Derived from Digital Elevation Models of the Loess Plateau, China

Although many studies have investigated slope gradient uncertainty derived from Digital Elevation Models(DEMs), the research concerning slope length uncertainty is far from mature. This discrepancy affects the availability and accuracy of soil erosion as well as hydrological modeling. This study investigates the formation and distribution of existing errors and uncertainties in slope length derivation based on 5-m resolution DEMs of the Loess Plateau in the middle of China. The slope length accuracy in three different landform areas is examined to analyse algorithm effects. The experiments indicate that the accuracy of the flat test area is lower than that of the rougher areas. The value from the specific contributing area(SCA) method is greater than the cumulative slope length(CSL), and the differences between these two methods arise from the shape of the upslope area. The variation of mean slope length derived from various DEM resolutions and landforms. The slope length accuracy decreases with increasing grid size and terrain complexity at the six test sites. A regression model is built to express the relationship of mean slope length with DEM resolution less than 85 m and terrain complexity represented by gully density. The results support the understanding of the slope length accuracy, thereby aiding in the effective evaluation of the modeling effect of surface process.

Model Uncertainty Representation for a Convection-Allowing Ensemble Prediction System Based on CNOP-P

Formulating model uncertainties for a convection-allowing ensemble prediction system(CAEPS)is a much more challenging problem compared to well-utilized approaches in synoptic weather forecasting.A new approach is proposed and tested through assuming that the model uncertainty should reasonably describe the fast nonlinear error growth of the convection-allowing model,due to the fast developing character and strong nonlinearity of convective events.The Conditional Nonlinear Optimal Perturbation related to Parameters(CNOP-P)is applied in this study.Also,an ensemble approach is adopted to solve the CNOP-P problem.By using five locally developed strong convective events that occurred in pre-rainy season of South China,the most sensitive parameters were detected based on CNOP-P,which resulted in the maximum variations in precipitation.A formulation of model uncertainty is designed by adding stochastic perturbations into these sensitive parameters.Through comparison ensemble experiments by using all the 13 heavy rainfall cases that occurred in the flood season of South China in 2017,the advantages of the CNOP-P-based method are examined and verified by comparing with the well-utilized stochastically perturbed physics tendencies(SPPT)scheme.The results indicate that the CNOP-P-based method has potential in improving the under-dispersive problem of the current CAEPS.

Modelling Uncertainty of Stream Networks Derived from Elevation Data Using Two Free Softwares: R and SAGA

Stream networks are considered important units in many environmental decision making processes. The extraction of streams using digital elevation models (DEMs) presents many advantages. However it is very sensitive to the uncertainty of the elevation datasets used. The main aim of this paper is to implement geostatistical simulations and assess the propagated uncertainty and map the error of location streams. First, point sampled elevations are used to fit a variogram model. Next two hundred DEM realizations are generated using conditional sequential Gaussian simulation;the stream network map is extracted for each of these realizations, and the collection of stream networks is analyzed to quantify the error propagation. At each grid cell, the probability of the occurrence of a stream and the propagated error are estimated. The more probable stream network are delineated and compared with the digital stream network derived from topographic map. The method is illustrated using a small dataset (8742 sampled elevations) for Anaguid Saharan platform. All computations are run in two free softwares: R and SAGA. R is used to fit variogram and to run sequential Gaussian simulation. SAGA is used to extract streams via RSAGA library.

Study on evaluation standard of uncertainty of design wave height calculation model

The accurate calculation of marine environmental design parameters depends on the probability distribution model,and the calculation results of different distribution models are often different.It is very important to determine which distribution model is more stable and reasonable when extrapolating the recurrence level of the studied sea area.In this paper,we constructed an evaluation method of the overall uncertainty of the calculation results and a measurement of the uncertainty of the design parameters derivation model,by incorporating the influence of sample information on the model information entropy,such as sample size,degree of dispersion,and sampling error.Results show that the sample data size and the degree of dispersion are directly proportional to the information entropy.Within the same group of data,the maximum entropy distribution model has the lowest overall uncertainty,while the Gumbel distribution model has the largest overall uncertainty.In other words,the maximum entropy distribution model has good applicability in the accurate calculation of marine environmental design parameters.

A Nonlinear Representation of Model Uncertainty in a Convective-Scale Ensemble Prediction System

How to accurately address model uncertainties with consideration of the rapid nonlinear error growth characteristics in a convection-allowing system is a crucial issue for performing convection-scale ensemble forecasts.In this study,a new nonlinear model perturbation technique for convective-scale ensemble forecasts is developed to consider a nonlinear representation of model errors in the Global and Regional Assimilation and Prediction Enhanced System(GRAPES)Convection-Allowing Ensemble Prediction System(CAEPS).The nonlinear forcing singular vector(NFSV)approach,that is,conditional nonlinear optimal perturbation-forcing(CNOP-F),is applied in this study,to construct a nonlinear model perturbation method for GRAPES-CAEPS.Three experiments are performed:One of them is the CTL experiment,without adding any model perturbation;the other two are NFSV-perturbed experiments,which are perturbed by NFSV with two different groups of constraint radii to test the sensitivity of the perturbation magnitude constraint.Verification results show that the NFSV-perturbed experiments achieve an overall improvement and produce more skillful forecasts compared to the CTL experiment,which indicates that the nonlinear NFSV-perturbed method can be used as an effective model perturbation method for convection-scale ensemble forecasts.Additionally,the NFSV-L experiment with large perturbation constraints generally performs better than the NFSV-S experiment with small perturbation constraints in the verification for upper-air and surface weather variables.But for precipitation verification,the NFSV-S experiment performs better in forecasts for light precipitation,and the NFSV-L experiment performs better in forecasts for heavier precipitation,indicating that for different precipitation events,the perturbation magnitude constraint must be carefully selected.All the findings above lay a foundation for the design of nonlinear model perturbation methods for future CAEPSs.