Impact of the Time Scale of Model Sensitivity Response on Coupled Model Parameter Estimation

That a model has sensitivity responses to parameter uncertainties is a key concept in implementing model parameter es- timation using filtering theory and methodology. Depending on the nature of associated physics and characteristic variability of the fluid in a coupled system, the response time scales of a model to parameters can be different, from hourly to decadal. Unlike state estimation, where the update frequency is usually linked with observational frequency, the update frequency for parameter estimation must be associated with the time scale of the model sensitivity response to the parameter being esti- mated. Here, with a simple coupled model, the impact of model sensitivity response time scales on coupled model parameter estimation is studied. The model includes characteristic synoptic to decadal scales by coupling a long-term varying deep ocean with a slow-varying upper ocean forced by a chaotic atmosphere. Results show that, using the update frequency deter- mined by the model sensitivity response time scale, both the reliability and quality of parameter estimation can be improved significantly, and thus the estimated parameters make the model more consistent with the observation. These simple model results provide a guideline for when real observations are used to optimize the parameters in a coupled general circulation model for improving climate analysis and prediction initialization.

Introducing the nth-Order Features Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (nth-FASAM-N): I. Mathematical Framework

This work presents the “nth-Order Feature Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (abbreviated as “nth-FASAM-N”), which will be shown to be the most efficient methodology for computing exact expressions of sensitivities, of any order, of model responses with respect to features of model parameters and, subsequently, with respect to the model’s uncertain parameters, boundaries, and internal interfaces. The unparalleled efficiency and accuracy of the nth-FASAM-N methodology stems from the maximal reduction of the number of adjoint computations (which are considered to be “large-scale” computations) for computing high-order sensitivities. When applying the nth-FASAM-N methodology to compute the second- and higher-order sensitivities, the number of large-scale computations is proportional to the number of “model features” as opposed to being proportional to the number of model parameters (which are considerably more than the number of features).When a model has no “feature” functions of parameters, but only comprises primary parameters, the nth-FASAM-N methodology becomes identical to the extant nth CASAM-N (“nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems”) methodology. Both the nth-FASAM-N and the nth-CASAM-N methodologies are formulated in linearly increasing higher-dimensional Hilbert spaces as opposed to exponentially increasing parameter-dimensional spaces thus overcoming the curse of dimensionality in sensitivity analysis of nonlinear systems. Both the nth-FASAM-N and the nth-CASAM-N are incomparably more efficient and more accurate than any other methods (statistical, finite differences, etc.) for computing exact expressions of response sensitivities of any order with respect to the model’s features and/or primary uncertain parameters, boundaries, and internal interfaces.

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.

Snow and sea ice thermodynamics in the Arctic:Model validation and sensitivity study against SHEBA data

Evolution of the Arctic sea ice and its snow cover during the SHEBA year were simulated by applying a high-resolution thermodynamic snow/ice model （HIGHTSI）. Attention was paid to the impact of albedo on snow and sea ice mass balance, effect of snow on total ice mass balance, and the model vertical resolution. The SHEBA annual simulation was made applying the best possible external forcing data set created by the Sea Ice Model Intercomparison Project. The HIGHTSI control run reasonably reproduced the observed snow and ice thickness. A number of albedo schemes were incorporated into HIGHTSI to study the feedback processes between the albedo and snow and ice thickness. The snow thickness turned out to be an essential variable in the albedo parameterization. Albedo schemes dependent on the surface temperature were liable to excessive positive feedback effects generated by errors in the modelled surface temperature. The superimposed ice formation should be taken into account for the annual Arctic sea ice mass balance.

Parameter sensitivity study of the biogeochemical model in the China coastal seas

In order to develop a coupled basin scale model of ocean circulation and biogeochemical cycling,we present a biogeochemical model including 12 components to study the ecosystem in the China coastal seas（CCS）.The formulation of phytoplankton mortality and zooplankton growth are modified according to biological characteristics of CCS.The four sensitivity biological parameters,zooplankton assimilation efficiency rate（ZooAE_N）,zooplankton basal metabolism rate（ZooBM）,maximum specific growth rate of zooplankton（μ_（20）） and maximum chlorophyll to carbon ratio（Chl2C_m） are obtained in sensitivity experiments for the phytoplankton,and experiments about the parameter μ_（20＇）,half-saturation for phytoplankton NO_3 uptake（K_（NO_3）） and remineralization rate of small detritusN（SDeRRN） are conducted.The results demonstrate that the biogeochemical model is quite sensitive to the zooplankton grazing parameter when it ranges from 0.1 to 1.2 d^（-1）.The K_（NO_3） and SDeRRN also play an important role in determining the nitrogen cycle within certain ranges.The sensitive interval of KNO_3 is from 0.1 to 1.5（mmol/m^3）^（-1）,and interval of SEdRRN is from 0.01 and 0.1 d^（-1）.The observational data from September 1998 to July 2000 obtained at SEATS station are used to validate the performance of biological model after parameters optimization.The results show that the modified model has a good capacity to reveal the biological process features,and the sensitivity analysis can save computational resources greatly during the model simulation.

Engineering Model for Detecting Sensitivity of the Coupling Capacitance Detector

The sensitivity engineering model of the coupling capacitance detector is built to provide the theoretic foundation for designing its circuits and electrodes scientifically. The sensitivity concept model of the capacitance proximity detector is discussed, and the detecting sensitivity of the coupling capacitance detector is analyzed theoretically. Then the sensitivity engineering model, which can reflect the main parameters relationship of the detecting circuit is set up based on the foregoing analyses. It is concluded that: ① the sensitivity is mainly correlative with some parameters including the voltage transmission factor of the demodulator, the oscillating voltage amplitude and the amplitude variation constant of the oscillator; ② the sensitivity is also influenced by the areas of electrodes and the distance between electrodes of the detector.

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.

Sensitivity of Statistical Models for Extremes Rainfall Adjustment Regarding Data Size: Case of Ivory Coast

The objective of this study is to analyze the sensitivity of the statistical models regarding the size of samples. The study carried out in Ivory Coast is based on annual maximum daily rainfall data collected from 26 stations. The methodological approach is based on the statistical modeling of maximum daily rainfall. Adjustments were made on several sample sizes and several return periods (2, 5, 10, 20, 50 and 100 years). The main results have shown that the 30 years series (1931-1960;1961-1990;1991-2020) are better adjusted by the Gumbel (26.92% - 53.85%) and Inverse Gamma (26.92% - 46.15%). Concerning the 60-years series (1931-1990;1961-2020), they are better adjusted by the Inverse Gamma (30.77%), Gamma (15.38% - 46.15%) and Gumbel (15.38% - 42.31%). The full chronicle 1931-2020 (90 years) presents a notable supremacy of 50% of Gumbel model over the Gamma (34.62%) and Gamma Inverse (15.38%) model. It is noted that the Gumbel is the most dominant model overall and more particularly in wet periods. The data for periods with normal and dry trends were better fitted by Gamma and Inverse Gamma.

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.

Proof of the Monotonicity of Grid Size and Its Application in Grid-Size Selection for Mesoscale Models

Terrain characteristics can be accurately represented in spectrum space. Terrain spectra can quantitatively reflect the effect of topographic dynamic forcing on the atmosphere. In wavelength space, topographic spectral energy decreases with decreasing wavelength, in spite of several departures. This relationship is approximated by an exponential function. A power law relationship between the terrain height spectra and wavelength is fitted by the least-squares method, and the fitting slope is associated with grid-size selection for mesoscale models. The monotonicity of grid size is investigated, and it is strictly proved that grid size increases with increasing fitting exponent, indicating that the universal grid size is determined by the minimum fitting exponent. An example of landslide-prone areas in western Sichuan is given, and the universal grid spacing of 4.1 km is shown to be a requirement to resolve 90% of terrain height variance for mesoscale models, without resorting to the parameterization of subgrid-scale terrain variance. Comparison among results of different simulations shows that the simulations estimate the observed precipitation well when using a resolution of 4.1 km or finer. Although the main flow patterns are similar, finer grids produce more complex patterns that show divergence zones, convergence zones and vortices. Horizontal grid size significantly affects the vertical structure of the convective boundary layer. Stronger vertical wind components are simulated for finer grid resolutions. In particular, noticeable sinking airflows over mountains are captured for those model configurations.

Sensitivities of Numerical Model Forecasts of Extreme Cyclone Events

A global forecast model is used to examine various sensitivities of numerical predictions of three extreme winter storms that occurred near the eastern continental margin of North America: the Ohio Valley blizzard of January 1978, the New England blizzard of February 1978, and the Mid-Atlantic cyclone of February 1979. While medium-resolution simulations capture much of the intensification, the forecasts of the precise timing and intensity levels suffer from various degrees of error. The coastal cyclones show a 5-10 hPa dependence on the western North Atlantic sea surface temperature, which is varied within a range (± 2.5℃) compatible with interannual fluctuations. The associated vertical velocities and precipitation rates show proportionately stronger dependences on the ocean temperature perturbations. The Ohio Valley blizzard, which intensified along a track 700-800 km from the coast, shows little sensitivity to ocean temperature. The effect of a shift of - 10?latitude in the position of the snow boundary is negligible in each case. The forecasts depend strongly on the model resolution, and the coarse-resolution forecasts are consistently inferior to the medium-resolution forecasts. Studies of the corresponding sensitivities of extreme cyclonic events over eastern Asia are encouraged in order to identify characteristics that are common to numerical forecasts for the two regions.

Analysis of Frequency Characteristics and Sensitivity of Compliant Mechanisms

Based on a modified pseudo-rigid-body model,the frequency characteristics and sensitivity of the large-deformation compliant mechanism are studied.Firstly,the pseudo-rigid-body model under the static and kinetic conditions is modified to enable the modified pseudo-rigid-body model to be more suitable for the dynamic analysis of the compliant mechanism.Subsequently,based on the modified pseudo-rigid-body model,the dynamic equations of the ordinary compliant four-bar mechanism are established using the analytical mechanics.Finally,in combination with the finite element analysis software ANSYS,the frequency characteristics and sensitivity of the compliant mechanism are analyzed by taking the compliant parallel-guiding mechanism and the compliant bistable mechanism as examples.From the simulation results,the dynamic characteristics of compliant mechanism are relatively sensitive to the structure size,section parameter,and characteristic parameter of material on mechanisms.The results could provide great theoretical significance and application values for the structural optimization of compliant mechanisms,the improvement of their dynamic properties and the expansion of their application range.

A Nine-layer Atmospheric General Circulation Model and Its Performance

Different versions of a new nine-layer general circulation model which is rhomboidally truncated at zonal wavenumber 15(L9R15)are introduced in this paper.On using the observed global monthly sea surfaCe temperature(SST)and sea ice(SI)data from 1979 to 1988 offered by the internahonal Atmospheric Model Iute-comparison Program(AMIP),these different model versions were integrated for the ten-year AMIP period. Results show that the model iscapable of simulating the basic states of the atmosphere and its interannual variability,and in performing reasonablesensitivity experiments.

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.

The Coordinated Influence of Indian Ocean Sea Surface Temperature and Arctic Sea Ice on Anomalous Northeast China Cold Vortex Activities with Different Paths during Late Summer

The Northeast China cold vortex(NCCV)during late summer(from July to August)is identified and classified into three types in terms of its movement path using machine learning.The relationships of the three types of NCCV intensity with atmospheric circulations in late summer,the sea surface temperature(SST),and Arctic sea ice concentration(SIC)in the preceding months,are analyzed.The sensitivity tests by the Community Atmosphere Model version 5.3(CAM5.3)are used to verify the statistical results.The results show that the coordination pattern of East Asia-Pacific(EAP)and Lake Baikal high pressure forced by SST anomalies in the North Indian Ocean dipole mode(NIOD)during the preceding April and SIC anomalies in the Nansen Basin during the preceding June results in an intensity anomaly for the first type of NCCV.While the pattern of high pressure over the Urals and Okhotsk Sea and low pressure over Lake Baikal during late summer-which is forced by SST anomalies in the South Indian Ocean dipole mode(SIOD)in the preceding June and SIC anomalies in the Barents Sea in the preceding April-causes the intensity anomaly of the second type.The third type is atypical and is not analyzed in detail.Sensitivity tests,jointly forced by the SST and SIC in the preceding period,can well reproduce the observations.In contrast,the results forced separately by the SST and SIC are poor,indicating that the NCCV during late summer is likely influenced by the coordinated effects of both SST and SIC in the preceding months.

在斜向非定常流动中由层流向湍流转变对模型尺度螺旋桨性能和压力脉动的影响

In this paper,after the successful applications to open water propeller performance estimations,the influence of transition sensitive and modified mass transfer models tuned to account for the laminar flow in the prediction of the cavitation inception of marine propulsors is investigated from the point of view of the unsteady functioning and induced pressure pulses.The VP1304(also known as PPTC)test case,for which dedicated data were collected during several workshops,is considered first.After preliminary analyses using RANS,also Detached Eddy Simulations(DES)are included to better account for the vortex dynamics and its influence on pressure pulses.Similarly to what observed in uniform inflow,results show a better agreement with the available measurements of propeller performances and confirm the reliability of the proposed approaches for unsteady,non-cavitating,model scale propeller predictions.The overall cavitation pattern is improved too by the application of the transition sensitive correction to the mass transfer model,but the complex dynamics of bubble cavitation observed in experiments prevents quantitatively better predictions in terms of thrust/torque breakdown and induced pressure pulses levels regardless the use of RANS or DES methods.

Accuracy Analysis and Design of A3 Parallel Spindle Head

As functional components of machine tools, parallel mechanisms are widely used in high efficiency machining of aviation components, and accuracy is one of the critical technical indexes. Lots of researchers have focused on the accuracy problem of parallel mechanisms, but in terms of controlling the errors and improving the accuracy in the stage of design and manufacturing, further efforts are required. Aiming at the accuracy design of a 3-DOF parallel spindle head（A3 head）, its error model, sensitivity analysis and tolerance allocation are investigated. Based on the inverse kinematic analysis, the error model of A3 head is established by using the first-order perturbation theory and vector chain method. According to the mapping property of motion and constraint Jacobian matrix, the compensatable and uncompensatable error sources which affect the accuracy in the end-effector are separated. Furthermore, sensitivity analysis is performed on the uncompensatable error sources. The sensitivity probabilistic model is established and the global sensitivity index is proposed to analyze the influence of the uncompensatable error sources on the accuracy in the end-effector of the mechanism. The results show that orientation error sources have bigger effect on the accuracy in the end-effector. Based upon the sensitivity analysis results, the tolerance design is converted into the issue of nonlinearly constrained optimization with the manufacturing cost minimum being the optimization objective. By utilizing the genetic algorithm, the allocation of the tolerances on each component is finally determined. According to the tolerance allocation results, the tolerance ranges of ten kinds of geometric error sources are obtained. These research achievements can provide fundamental guidelines for component manufacturing and assembly of this kind of parallel mechanisms.

Anthropogenic Source Contributions to Ozone Formation in the Greater Houston Area

The Houston-Galveston-Brazoria (HGB) area of Texas has historically experienced severe air pollution events with high concentrations of ozone (O3) during the summer season. This study evaluates the contribution of different anthropogenic sources to ozone formation in the HGB area. The Emission Processing System (EPS3) is used to process emission files in four different scenarios (Base case as including All emission sources (BC), All sources— Area sources (AMA), All sources—Point sources (AMP), and All sources— Mobile sources (AMM). These files are used as input in photochemical modeling with the Comprehensive Air Quality Model with Extensions (CAMx) to simulate ozone formation. The data is analyzed for daily maximum ozone concentrations and contribution of source categories at three air quality monitoring locations (La Porte Sylvan beach-C556, Houston Texas avenue-C411, and Texas city in Galveston-C683) for a study period of June 1-June 30, 2012. The contribution of the point sources to ozone formation is dominated at all three locations, followed by mobile sources and area sources on high ozone days. The relative contributions of point sources are 27.51% ± 3.53%, 21.45% ± 7.36%, and 30.30% ± 9.36%;and mobile sources are 18.27% ± 2.22%, 20.60% ± 6.89%, and 18.61% ± 7.43%;and area sources were 4.2% ± 1.65%, 5.21% ± 1.59%, and 3.72% ± 1.52% at C556, C411, and C683, respectively. These results demonstrate the importance of regulatory focus on controlling point and mobile source emissions for NAAQS attainment in the study region.

Population Viability Analysis of Gloydius shedaoensis from Northeastern China:A Contribution to the Assessment of the Conservation and Management Status of an Endangered Species

Shedao pit-vipers(Gloydius shedaoensis) on Snake Island in the Liaoning Province, China, are among the most imperiled species in China. The isolated and unique populations are crucial in the recovery of this endangered species by providing a way for conservation and management. Research based on the ecological simulation tools can evaluate alternative mitigation strategies in terms of their benefits to the populations, which are vital for informed decision-making. In this paper, using the program VORTEX 9.42, we developed a population viability analysis(PVA) for the Shedao pit-viper to:(1) address the extinction likelihood of the population;(2) simulate population dynamics under various environment events, and(3) evaluate the efficacy of current protection and management strategies. Overall, we found the population to be susceptible to the factors of catastrophic events, mortality and environment capacity. The population is recovering slowly at present on account of improvement of habitat and greater food availability. Under the current conditions, the probability of extinction in 100 years is approximately zero. These data coincide with the evidence that the wild population may be arriving at K. Our results strengthen the view that protection and management can create a pronounced effect on populations of this endangered species.

大尺度跨境流域径流预测的迁移学习框架--敏感性分析及在数据稀缺流域的适用性

The imbalance in global streamflow gauge distribution and regional data scarcity,especially in large transboundary basins,challenge regional water resource management.Effectively utilizing these limited data to construct reliable models is of crucial practical im-portance.This study employs a transfer learning(TL)framework to simulate daily streamflow in the Dulong-lrrawaddy River Basin(DIRB),a less-studied transboundary basin shared by Myanmar,China,and India.Our results show that TL significantly improves streamflow pre-dictions:the optimal TL model achieves an average Nash-Sutcliffe efficiency of 0.872,showing a marked improvement in the Hkamti sub-basin.Despite data scarcity,TL achieves a mean NSE of 0.817,surpassing the 0.655 of the process-based model MIKE SHE.Addition-ally,our study reveals the importance of source model selection in TL,as different parts of the flow are affected by the diversity and similarity of data in the source model.Deep learning models,particularly TL,exhibit complex sensitivities to meteorological inputs,more accu-rately capturing non-linear relationships among multiple variables than the process-based model.Integrated gradients(IG)analysis furtherillustrates TL's ability to capture spatial het-erogeneity in upstream and downstream sub-basins and its adeptness in characterizing dif-ferent flow regimes.This study underscores the potential of TL in enhancing the under-standing of hydrological processes in large-scale catchments and highlights its value for wa-ter resource management in transboundary basins under data scarcity.