Assessment of the three representative empirical models for zenith tropospheric delay(ZTD)using the CMONOC data

The precise correction of atmospheric zenith tropospheric delay(ZTD)is significant for the Global Navigation Satellite System(GNSS)performance regarding positioning accuracy and convergence time.In the past decades,many empirical ZTD models based on whether the gridded or scattered ZTD products have been proposed and widely used in the GNSS positioning applications.But there is no comprehensive evaluation of these models for the whole China region,which features complicated topography and climate.In this study,we completely assess the typical empirical models,the IGGtropSH model(gridded,non-meteorology),the SHAtropE model(scattered,non-meteorology),and the GPT3 model(gridded,meteorology)using the Crustal Movement Observation Network of China(CMONOC)network.In general,the results show that the three models share consistent performance with RMSE/bias of 37.45/1.63,37.13/2.20,and 38.27/1.34 mm for the GPT3,SHAtropE and IGGtropSH model,respectively.However,the models had a distinct performance regarding geographical distribution,elevation,seasonal variations,and daily variation.In the southeastern region of China,RMSE values are around 50 mm,which are much higher than that in the western region,approximately 20 mm.The SHAtropE model exhibits better performance for areas with large variations in elevation.The GPT3 model and the IGGtropSH model are more stable across different months,and the SHAtropE model based on the GNSS data exhibits superior performance across various UTC epochs.

Empirical modeling of normal/cyclo-alkanes pyrolysis to produce light olefins

Due to the complexity of feedstock,it is challenging to build a general model for light olefins production.This work was intended to simulate the formation of ethylene,propene and 1,3-butadiene in alkanes pyrolysis by referring the effects of normal/cyclo-structures.First,the pyrolysis of n-pentane,n-hexane,n-heptane,n-octane,n-nonane,n-decane,cyclohexane,methylcyclohexane,n-hexane and cyclohexane mixtures,and n-heptane and methylcyclohexane mixtures were carried out at 650–800℃,and a particular attention was paid to the measurement of ethylene,propene and 1,3-butadiene.Then,pseudo-first order kinetics was taken to characterize the pyrolysis process,and the effects of feedstock composition were studied.It was found that chain length and cyclo-alkane content can be qualitatively and quantitively represented by carbon atom number and pseudo-cyclohexane content,which made a significant difference on light olefins formation.Furthermore,the inverse proportional/quadratic function,linear function and exponential function were proposed to simulate the effects of chain length,cycloalkane content and reaction temperature on light olefins formation,respectively.Although the obtained empirical model well reproduced feedstock conversion,ethylene yield and propene yield in normal/cycloalkanes pyrolysis,it exhibited limitations in simulating 1,3-butadiene formation.Finally,the accuracy and flexibility of the present model was validated by predicting light olefins formation in the pyrolysis of multiple hydrocarbon mixtures.The prediction data well agreed with the experiment data for feedstock conversion,ethylene yield and propene yield,and overall characterized the changing trend of 1,3-butadiene yield along with reaction temperature,indicating that the present model could basically reflect light olefins production in the pyrolysis process even for complex feedstock.

Statistical prediction of waterflooding performance by K-means clustering and empirical modeling

Statistical prediction is often required in reservoir simulation to quantify production uncertainty or assess potential risks.Most existing uncertainty quantification procedures aim to decompose the input random field to independent random variables,and may suffer from the curse of dimensionality if the correlation scale is small compared to the domain size.In this work,we develop and test a new approach,K-means clustering assisted empirical modeling,for efficiently estimating waterflooding performance for multiple geological realizations.This method performs single-phase flow simulations in a large number of realizations,and uses K-means clustering to select only a few representatives,on which the two-phase flow simulations are implemented.The empirical models are then adopted to describe the relation between the single-phase solutions and the two-phase solutions using these representatives.Finally,the two-phase solutions in all realizations can be predicted using the empirical models readily.The method is applied to both 2D and 3D synthetic models and is shown to perform well in the P10,P50 and P90 of production rates,as well as the probability distributions as illustrated by cumulative density functions.It is able to capture the ensemble statistics of the Monte Carlo simulation results with a large number of realizations,and the computational cost is significantly reduced.

An Empirical Model for Estimating Stratospheric Ozone Vertical Distributions over China

Based on the Stratospheric Aerosol and Gas Experiment （SAGE） Ⅱ and the Halogen Occultation Experiment （HALOE） ozone profiles and the Total Ozone Mapping Spectrometer （TOMS） total ozone data sets, an empirical model for estimating the vertical distribution of stratospheric ozone over China is proposed. By using this model, the vertical distribution of stratospheric （16-50 km） ozone can be estimated according to latitude, month and total ozone. Comparisons are made between the modeled ozone profiles and the SAGEII/HALOE monthly mean ozone measurements, and the results show that the model calculated ozone concentrations conform well with the SAGEII/HALOE measured values, with the differences being less than 15% between 16 km and 18 km, less than 5% between 19 km and 40 km, and less than 10% between 41 km and 50 kin. Comparisons of the model results with balloon-borne ozonesonde measurements performed in Beijing also show good agreement, within 5%, at altitudes between 19 km and 30 km.

An Empirical Model for Estimating the Zonal Mean Aerosol Extinction Profiles from SAGE II Measurements

This paper presents an empirical model for estimating the zonal mean aerosol extinction profiles in the stratosphere over 10°-wide latitude bands between 60°S and 60°N, on the basis of Stratospheric Aerosol and Gas Experiment(SAGE) II aerosol extinction measurements at 1.02, 0.525, and 0.452 μm during the volcanically quiescent period between 1998–2004. First, an empirical model is developed for calculating the stratospheric aerosol extinction profiles at 1.02 μm. Then, starting from the 1.02 μm extinction profile and an exponential spectral dependence, an empirical algorithm is developed that allows the aerosol extinction profiles at other wavelengths to be calculated. Comparisons of the model-calculated aerosol extinction profiles at the wavelengths of 1.02, 0.525, and 0.452 μm and the SAGE II measurements show that the model-calculated aerosol extinction coefficients conform well with the SAGE II values, with the relative differences generally being within 15% from 2 km above the tropopause to 40 km. The model-calculated stratospheric aerosol optical depths at the three wavelengths are also in good agreement with the corresponding optical depths derived from the SAGE II measurements, with the relative differences being within 0.9% for all latitude bands. This paper provides a useful tool in simulating zonal mean aerosol extinction profiles, which can be used as representative background stratospheric aerosols in view of atmospheric modeling and remote sensing retrievals.

Empirical Models for the Evaluation of Global Solar Radiation for the Site of Abeche in the Province of Ouaddaï, in Chad

The global sustainability plan for future development relies on solar radiation which is the main source of renewable energy. Thus, this work studies the performance of six models to estimate global solar radiation on a horizontal surface for the Abeche site in Chad. The data used in this work were collected at the General Directorate of National Meteorology of Chad. The reliability and accuracy of different models for estimating global solar radiation were validated by statistical indicators to identify the most accurate model. The results show that among all the models, the Sabbagh model has the best performance in estimating the global solar radiation. The average is 6.354 kWh/m2 with an average of -3.704%. This model is validated against NASA data which is widely used.

Anisotropic time-dependent behaviors of shale under direct shearing and associated empirical creep models

Understanding the anisotropic creep behaviors of shale under direct shearing is a challenging issue.In this context,we conducted shear-creep and steady-creep tests on shale with five bedding orientations (i.e.0°,30°,45°,60°,and 90°),under multiple levels of direct shearing for the first time.The results show that the anisotropic creep of shale exhibits a significant stress-dependent behavior.Under a low shear stress,the creep compliance of shale increases linearly with the logarithm of time at all bedding orientations,and the increase depends on the bedding orientation and creep time.Under high shear stress conditions,the creep compliance of shale is minimal when the bedding orientation is 0°,and the steady-creep rate of shale increases significantly with increasing bedding orientations of 30°,45°,60°,and 90°.The stress-strain values corresponding to the inception of the accelerated creep stage show an increasing and then decreasing trend with the bedding orientation.A semilogarithmic model that could reflect the stress dependence of the steady-creep rate while considering the hardening and damage process is proposed.The model minimizes the deviation of the calculated steady-state creep rate from the observed value and reveals the behavior of the bedding orientation's influence on the steady-creep rate.The applicability of the five classical empirical creep models is quantitatively evaluated.It shows that the logarithmic model can well explain the experimental creep strain and creep rate,and it can accurately predict long-term shear creep deformation.Based on an improved logarithmic model,the variations in creep parameters with shear stress and bedding orientations are discussed.With abovementioned findings,a mathematical method for constructing an anisotropic shear creep model of shale is proposed,which can characterize the nonlinear dependence of the anisotropic shear creep behavior of shale on the bedding orientation.

An empirical model for high energy density lithium-(ion)batteries with ultra-thick electrodes

Increasing the electrode thickness is a significant method to decrease the weight and volume ratio of the inactive components for high energy density of the devices.In this contribution,we extracted a repeating unit in the configurations and establish the empirical energy density model based on some assumptions.In this model,the effects of the electrode thickness on the energy density for lithium-ion batteries(LIBs),lithium metal batteries(LMBs),and anode-free lithium batteries(ALBs)are evaluated quantitively with the current parameters of the batteries.The results demonstrate that the structure evolutions from LIBs,LMBs to ALBs with the reduction of the anode weight contribution,the energy density can be well improved exactly.While the increase of the thickness of the electrode provide another route to furthe r enhance the energydensity by decreasing the weight contribution of inactive materials;meanwhile the effects for ALBs are higher than LMBs and LIBs due to the higher weight ratio of inactive materials.This empirical energy density model is also applied into the practical system and provide intuitional results to guide the battery design for higher energy density.

Empirical model of concrete block fragment behavior under explosion loads

Concrete structures undergo integral fragmentation under explosion loads. The fragmentation degree and particle-size distribution of concrete blocks under explosion loads must be considered during mining to ensure safety. In this study, the impulse is calculated based on the relationship between overpressure and time, and the impact energy of the explosion wave is obtained based on blast theory. Subsequently, the Mohr-Coulomb shear strength fracture criterion is introduced to determine the ultimate shear stress of the concrete materials, and an empirical model that can effectively calculate the energy consumption of concrete blocks under explosion loads is established. Furthermore, concrete fragments with different particle sizes under explosion scenarios are quantitatively predicted with the principle of energy conservation. Finally, explosion tests with different top standoff distances are conducted, and the concrete fragments after the explosion tests are recovered, sieved, weighed, and counted to obtain experimental data. The effectiveness of the fragment empirical model is verified by comparing the model calculation results with the experimental data. The proposed model can be used as a reference for civil blasting, protective engineering design, and explosion-damage assessment.

Pyrolysis Empirical Modeling of Polyester Glass Fiber Reinforced Plastics Using Sestak-Berggren Model Method

Polyester Glass Fiber Reinforced Plastic(Polyester GFRP),a thermosetting plastic comprised of glass fiber and polyester polymer compounds,is extensively utilized in high-speed trains.Unraveling its pyrolysis mechanism is crucial as it significantly influences the combustion characteristics and fire safety aspects.Currently,kinetic research on polyester GFRP primarily focuses on employing the Coats-Redfern method to derive a theoretical kinetic model.However,the pyrolysis process of polyester GFRP is complex and the aforementioned theoretical model fails to accurately describe the pyrolysis mechanism.Therefore,this study seeks to utilize the Sestak and Berggren(SB) model as a methodological approach to reveal the complex reaction mechanism during the pyrolysis process.Based on thermogravimetric analysis,the entire pyrolysis process of polyester GFRP is divided into two primary stages.Furthermore,model-free methods are employed to ascertain the activation energy and pre-exponential factor.The results show that the fitted empirical models of the two main pyrolysis stages are f(α)=(1-α)^(1.47)[-ln(1-α)]^(1.50) and f(α)=(1-α)^(1.77)[-ln(1-α)]^(1.72),respectively.The predicted results are in good agreement with experimental data under different heating rates,which indicates that the empirical model can sufficiently describe the pyrolysis process of polyester GFRP.

A New Empirical Large Signal Model of 4H-SiC MESFETs for the Nonlinear Analysis

A new comprehensive empirical large signal model for 4H-SiC MESFETs is proposed. An enhanced drain current model,along with an improved charge conservation capacitance model,is presented by the improvement of the channel length modulation and the hyperbolic tangent function coefficient based on the Materka model. The Levenberg-Marquardt method is used to optimize the parameter extraction. A comparison of simulation resuits with experimental data is made,and good agreements of I-V curves, Pout （output power）, PAE （power added efficiency） ,and gain at the bias of Vos = 20V, Ips = 80mA as well as the operational frequency of 1.8GHz are obtained.

Application of New Empirical Models Based on Mathematical Statistics in the Through-Flow Analysis

The through-flow analysis is an important part in the compressor design process.In this part,lots of empirical models are used to predict the compressor aerodynamic performances.These models are all based on the early experimental results of low-load and low-speed compressors;so,they may not be suitable for modern compressor performance estimations.In this study,several empirical models were reviewed,and two new models to estimate the minimum blade profile loss and minimum-loss deviation angle were established using mathematical statistics.Then,the original models with poor accuracy were replaced by these two models in through-flow program.Next,three compressors(Rotor 67,Stage 35,and a 4-stage repeating stage)were simulated using both the original and new models.The final results show that the new models have better accuracy in estimating the performance parameters than the original models.This indicates that it is feasible to use mathematical statistical methods to establish the empirical models,and this method provides an idea for the improvement of other empirical models in through-flow program.

Empirical modeling of ionospheric F2 layer critical frequency over Wakkanai under geomagnetic quiet and disturbed conditions

The hourly values of the ionospheric F2 layer critical frequency, foF2, recorded at Wakkanai ionosonde station （45.4°N, 141.7°E） have been collected to construct a middle-latitude single-station model for forecasting foF2 under geomagnetic quiet and disturbed conditions. The module for the geomagnetic quiet conditions incorporates local time, seasonal, and solar vari- ability of climatological foF2 and its upper and lower quartiles. It is the first attempt to predict the upper and lower quartiles of foF2 to account for the notable day-to-day variability in ionospheric foF2. The validation statistically verifies that the model captures the climatological variations of foF2 with higher accuracy than IRI does. The storm-time module is built to capture the geomagnetic storm induced relative deviations of foF2 from the quiet time references. In the geomagnetically disturbed module, the storm-induced deviations are described by diumal and semidiumal waves, which are modulated by a modified magnetic activity index, the Kf index, reflecting the delayed responses of foF2 to geomagnetic activity forcing. The coeffi- cients of the model in each month are determined by fitting the model formula to the observation in a least-squares way. We provide two options for the geomagnetic disturbed module, including or not including Kalman filter algorithm. The Kalman filter algorithm is introduced to optimize these coefficients in real time. Our results demonstrate that the introduction of the Kalman filter algorithm in the storm time module is promising for improving the accuracy of predication. In addition, comparisons indicate that the IRI model prediction of the F2 layer can be improved to provide better performances over this region.

Evolution and Development of the Information Concept in Biological Systems: From Empirical Description to Informational Modeling of the Living Structures

With the purpose to smooth the way of a correct understanding of information concepts and their evolution,in this paper,is discussed the evolution and development of the concept of information in biological systems,showing that this concept was intuitively perceived even since ancient times by our predecessors,and described according to their language level of that times,but the crystallization of the real meaning of information is an achievement of our nowadays,by successive contribution of various scientific branches and personalities of the scientific community of the world,leading to a modern description/modeling of reality,in which information plays a fundamental role.It is shown that our reality can be understood as a contribution of matter/energy/information and represented/discussed as the model of the Universal Triangle of Reality(UTR),where various previous models can be suggestively inserted,as a function of their basic concern.The modern concepts on information starting from a theoretic experiment which would infringe the thermodynamics laws and reaching the theory of information and modern philosophic concepts on the world structuration allow us to show that information is a fundamental component of the material world and of the biological structures,in correlation with the structuration/destructuration processes of matter,involving absorption/release of information.Based on these concepts,is discussed the functionality of the biologic structures and is presented the informational model of the human body and living structures,as a general model of info-organization on the entire biological scale,showing that a rudimentary proto-consciousness should be operative even at the low-scale biological systems,because they work on the same principles,like the most developed bio-systems.The operability of biologic structures as informational devices is also pointed out.

Development of EMC-based empirical model for estimating spatial distribution of pollutant loads and its application in rural areas of Korea

An integrated approach to easily calculate pollutant loads from agricultural watersheds is suggested and verified in this research. The basic concepts of this empirical tool were based on the assumption that variations in event mean concentrations（EMCs） of pollutants from a given agricultural watershed during rainstorms were only attributable to the rainfall pattern.Fifty one sets of EMC values were obtained from nine different watersheds located in the rural areas of Korea, and these data were used to develop predictive tools for the EMCs in rainfall runoff. The results of statistical tests of these formulas show that they are fairly good in predicting actual EMC values of some parameters, and useful in terms of calculating pollutant loads for any rainfall event time span such as daily, weekly, monthly, and yearly. This model was further checked in for its field applicability in a reservoir receiving stormwater after a cleanup of the sediments, covering 17 consecutive rainfall events from 1 July to 15 August in2007. Overall the predicted values matched the observed values, indicating the feasibility of this empirical tool as a simple and useful solution in evaluating timely distribution of nonpoint source pollution loads from small rural watersheds of Korea.

Prediction of salinity intrusion in the sheltered estuary of Terengganu River in Malaysia using 1-D empirical intrusion model

Generally one dimensional （l-D） empirical salinity intrusion model is limited to natural alluvial estuary. However, this study attempts to investigate its ability to model a sheltered alluvial estuary of the Terengganu River in Malaysia. The constructed breakwater at the mouth of the river shelters the estuary from direct influence of the open sea. The salinity density along the estuary was collected during the wet and dry seasons for scenarios before and after the constructed breakwater. Moreover, the freshwater discharges, tidal elevations and bathymetry data were also measured as model inputs. A good fit was demonstrated between simulated and observed variables, namely salinity distribution and intrusion length for both scenarios. Thus, the results show that 1-D empirical salinity model can be utilized for sheltered estuarine condition at the Terengganu Estuary, but with an appropriate determination of an initial point. Furthermore, it was observed that the salinity intrusion in the study area is largely dependent on the freshwater discharge rather than tidal elevation fluctuations. The scale of the salinity intrusion length in the study area is proportional to the river discharge of the -1/2 power. It was appeared that the two lines of the 1-D empirical salinity model and discharge power based equation fitted well to each other, with the average predicted minimum freshwater discharge of 150 m^3/s is going to be required to maintain acceptable salinity levels during high water slack （HWS） near the water intake station, which is located at 10.63 km from river mouth.

Novel empirical model for predicting residual flexural capacity of corroded steel reinforced concrete beam

In this study,a total of 177 flexural experimental tests of corroded reinforced concrete(CRC)beams were collected from the published literature.The database of flexural capacity of CRC beam was established by using unified and standardized experimental data.Through this database,the effects of various parameters on the flexural capacity of CRC beams were discussed,including beam width,the effective height of beam section,ratio of strength between longitudinal reinforcement and concrete,concrete compressive strength,and longitudinal reinforcement corrosion ratio.The results indicate that the corrosion of longitudinal reinforcement has the greatest effect on the residual flexural capacity of CRC beams,while other parameters have much less effect.In addition,six available empirical models for calculating the residual flexural strength of CRC beams were also collected and compared with each other based on the established database.It indicates that though five of six existing empirical models underestimate the flexural capacity of CRC beams,there is one model overestimating the flexural capacity.Finally,a newly developed empirical model is proposed to provide accurate and effective predictions in a large range of corrosion ratio for safety assessment of flexural failure of CRC beams confirmed by the comparisons.

Skillful prediction of winter Arctic Oscillation from previous summer in a linear empirical model

The winter Arctic Oscillation(WAO),as a primary atmospheric variability mode in the Northern Hemisphere,plays a key role in influencing mid-high-latitude climate variations.However,current dynamical seasonal forecasting systems have limited skills in predicting WAO with lead time longer than two months.In this study,we design a linear empirical model using two effective precursors from anomalies of the Arctic sea ice concentration(SIC)and the tropical sea surface temperature(SST)initiated in preceding late summer(August)which are both significantly correlated with WAO in recent four decades.This model can provide a skillful prediction of WAO at about half-year lead started from previous summer and perform much better than the dynamical models.Such a significantly prolonged lead time is owed to the stable precursor signals extracted from the SIC and SST anomalies over specific areas,which can persist from previous August and be further enhanced through autumn months.Validation results show that this model can produce a 20-year independent-validated prediction skill of 0.45 for 1999–2018 and a 39-year cross-validated skill of 0.67 for 1980–2018,providing a potentially effective tool for earlier predictions of winter climate variations at mid-high latitudes.

Efficient calculation of fluid-induced wall shear stress within tissue engineering scaffolds by an empirical model

Mechanical stimulation,such as fluid-induced wall shear stress(WSS),is known that can influence the cellular behaviours.Therefore,in some tissue engineering experiments in vitro,mechanical stimulation is applied via bioreactors to the cells in cell culturing to study cell physiology and pathology.In 3D cell culturing,porous scaffolds are used for housing the cells.It is known that the scaffold porous geometries can influence the scaffold permeability and internal WSS in a bioreactor(such as perfusion bioreactor).To calculate the WSS generated on cells within scaffolds,usually computational fluid dynamics(CFD)simulation is needed.However,the limitations of the computational method for WSS calculation are:(i)the high time cost of the CFD simulation(in particular for the highly irregular geometries);(ii)accessibility to the CFD model for some cell culturing experimentalists due to the knowledge gap.To address these limitations,this study aims to develop an empirical model for calculating the WSS based on scaffold permeability.This model can allow the tissue engineers to efficiently calculate the WSS generated within the scaffold and/or determine the bioreactor loading without performing the computational simulations.

Continuity of the robustness of contextuality of empirical models

Recently, the robustness of contextuality(RoC) of an empirical model was discussed in [Sci. China-Phys. Mech. Astron. 59,640303(2016)], many important properties of the RoC have been proved except for its boundedness and continuity. The aim of this paper is to find an upper bound for the RoC over all of empirical models and prove that the RoC is a continuous function on the set of all empirical models. Lastly, a relationship between the RoC and the extent of violating the noncontextual inequalities is established for an n-cycle contextual box. This relationship implies that the RoC can be used to quantify the contextuality of n-cycle boxes.