Spatiotemporal Characteristics of Reference Evapotranspiration and Its Sensitivity Coefficients to Climate Factors in Huang-Huai-Hai Plain,China

Climate change will have important implications in water shore regions,such as Huang-Huai-Hai（3H） plain,where expected warmer and drier conditions might augment crop water demand.Sensitivity analysis is important in understanding the relative importance of climatic variables to the variation in reference evapotranspiration（ET 0）.In this study,the 51-yr ET 0 during winter wheat and summer maize growing season were calculated from a data set of daily climate variables in 40 meteorological stations.Sensitivity maps for key climate variables were estimated according to Kriging method and the spatial pattern of sensitivity coefficients for these key variables was plotted.In addition,the slopes of the linear regression lines for sensitivity coefficients were obtained.Results showed that ET 0 during winter wheat growing season accounted for the largest proportion of annual ET 0,due to its long phenological days,while ET 0 was detected to decrease significantly with the magnitude of 0.5 mm yr-1in summer maize growing season.Solar radiation is considered to be the most sensitive and primarily controlling variable for negative trend in ET 0 for summer maize season,and higher sensitive coefficient value of ET 0 to solar radiation and temperature were detected in east part and southwest part of 3H plain respectively.Relative humidity was demonstrated as the most sensitive factor for ET 0 in winter wheat growing season and declining relativity humidity also primarily controlled a negative trend in ET 0,furthermore the sensitivity coefficient to relative humidity increased from west to southeast.The eight sensitivity centrals were all found located in Shandong Province.These ET 0 along with its sensitivity maps under winter wheat-summer maize rotation system can be applied to predict the agricultural water demand and will assist water resources planning and management for this region.

Irradiation effect on strain sensitivity coefficient of strain sensing fiber Bragg gratings

The effect of irradiation on the strain sensitivity coefficient of strain sensing fiber Bragg gratings （FBGs） has been investigated through experiments. FBGs were fabricated in single mode fibers with 3 tool% Ge-concentration in the core and with a H2-1oading treatment. In experiments, the FBGs were subjected to y-radiation exposures using a Co6~ source at a dose-rate of 25 Gy/min up to a total dose of 10.5 kGy. The GeO defect in fiber absorbs photons to form a GeE＇ defect; the interaction with H2 is a probable reason for the y-radiation sensitivity of gratings written in hydrogen loaded fibres, The effect mechanism of radiation on the strain sensitivity coefficient is similar to that of radiation on the temperature sensitivity coefficient. Radiation affects the effective index neff, which results in the change of the thermo-optic coefficient and the strain-optic coefficient. Irradiation can change the strain sensitivity coefficient of FBGs by 1.48%-2.71%, as well as changing the Bragg wavelength shift （BWS） by 22 pm-25 pm under a total dose of 10.5 kGy. Our research demonstrates that the effect of irradiation on the strain sensitivity coefficient of FBG is small and that strain sensing FBGs can work well in the radiation environment.

Reliability Sensitivity-based Correlation Coefficient Calculation in Structural Reliability Analysis

The correlation coefficients of random variables of mechanical structures are generally chosen with experience or even ignored,which cannot actually reflect the effects of parameter uncertainties on reliability.To discuss the selection problem of the correlation coefficients from the reliability-based sensitivity point of view,the theory principle of the problem is established based on the results of the reliability sensitivity,and the criterion of correlation among random variables is shown.The values of the correlation coefficients are obtained according to the proposed principle and the reliability sensitivity problem is discussed.Numerical studies have shown the following results：（1） If the sensitivity value of correlation coefficient ρ is less than（at what magnitude 0.000 01）,then the correlation could be ignored,which could simplify the procedure without introducing additional error.（2） However,as the difference between ρs,that is the most sensitive to the reliability,and ρR,that is with the smallest reliability,is less than 0.001,ρs is suggested to model the dependency of random variables.This could ensure the robust quality of system without the loss of safety requirement.（3） In the case of ｜Eabs｜ρ0.001 and also ｜Erel｜ρ0.001,ρR should be employed to quantify the correlation among random variables in order to ensure the accuracy of reliability analysis.Application of the proposed approach could provide a practical routine for mechanical design and manufactory to study the reliability and reliability-based sensitivity of basic design variables in mechanical reliability analysis and design.

Temporal and Spatial Variations of ET 0 and Sensitivity Coefficients in Spring-summer in Eastern Agricultural Areas of Qinghai,China

Reference crop evapotranspiration(ET 0) is a key parameter to calculate crop water requirements.In the paper,ET 0 during 1960-2005 was calculated with FAO-56 PM in eastern agricultural areas of Qinghai,China.Then the sensitivity coefficients of ET 0 to meteorological variables were estimated through the nondimensional partial derivative in FAO-56 PM.Results show that the mean annual ET 0 of the whole area is 904 mm,and ET 0 portrays a very significant decrease during the 46 years.In spatial,ET 0 decreases from southeast to northwest,firstly increases then decreases from southwest to northeast.Through sensitivity analysis,in spring the most sensitive variable is relative humidity,while in summer is temperature.The temperature,sunshine duration and wind speed sensitivity coefficients(S(TA),S(n),S(u)) are higher in middle areas as opposed to surrounding areas,while the relative humidity sensitivity coefficient(S(RH)) has an opposite distribution rule.

The Interstorey Drift Sensitivity Coefficient in Calculating Seismic Building Frames

In calculating the seismic response of a building, the Spanish Instructions NCSE-02 and CTE, paragraph 3.7.7 （also EUROCODE 8 paragraph 1.2 part 1-1）, establish that if for all storeys the interstorey drift sensitivity coefficient, ζ, is less than or equal to 0.1, then it will not be necessary to consider the effects of the 2nd order （ P-△ effects）. In this paper the authors review this claim, because even for ≤0.1, increases of the bending moment at the ends of the columns due to the inclusion of second order effects can account for between 15% and 34% of its value for static service loads. This is significant since most adverse effects are shown in the lower height buildings （up to 5 floors） which it is precisely the range in which most of the housing stock of Spain is located. Finally, the authors delimit the coefficient for buildings of lesser height （up to 5 floors）, proposing to lower it generally to ζ≤ 006.

SENSITIVITY COEFFICIENTS OF SINGLE-PHASE FLOW IN LOW-PERMEABILITY HETEROGENEOUS RESERVOIRS

Theoretical equations for computing sensitivity coefficients of wellbore pressures to estimate the reservoir parameters in low-permeability reservoirs conditioning to non-Darcy flow data at low velocity were obtained. It is shown by a lot of numerical calculations that the wellbore pressures are much more sensitive to permeability very near the well than to permeability a few gridblocks away from the well. When an initial pressure gradient existent sensitivity coefficients in the region are closer to the active well than to the observation well. Sensitivity coefficients of observation well at the line between the active well and the observation well are influenced greatly by the initial pressure gradient.

Soil Pressure Mini-sensor Made of Monocrystalline Silicon and the Measurement of Its Sensitivity Coefficient

A calibration test was done in order to measure its sensitivity coefficient by an improved soil test device.The experimental result shows that the soil pressure min-sensor made of the monocrystalline silicon（SPMMS）is proved to be good linear,high precision and less that can fetch precise data in low pressure range even near by O point,which guarantees the reliability of the soil pressure test in geotechnical engineering.

Chebyshev Polynomial-Based Analytic Solution Algorithm with Efficiency, Stability and Sensitivity for Classic Vibrational Constant Coefficient Homogeneous IVPs with Derivative Orders n, n-1, n-2

The Chebyshev polynomials are harnessed as functions of the one parameter of the nondimensionalized differential equation for trinomial homogeneous linear differential equations of arbitrary order n that have constant coefficients and exhibit vibration. The use of the Chebyshev polynomials allows calculation of the analytic solutions for arbitrary n in terms of the orthogonal Chebyshev polynomials to provide a more stable solution form and natural sensitivity analysis in terms of one parameter and the initial conditions in 6n + 7 arithmetic operations and one square root.

Sensitivity of Penman-Monteith Reference Crop Evapotranspiration in Tao'er River Basin of Northeastern China

A non-dimensional relative sensitivity coefficient was employed to predict the responses of reference crop evapotranspiration (ET0) to perturbation of four climate variables in Tao'er River Basin of the northeastern China. Mean monthly ET0 and yearly ET0 from 1961 to 2005 were estimated with the FAO-56 Penman-Monteith Equation. A 45-year historical dataset of average monthly maximum/minimum air temperature, mean air temperature, wind speed, sunshine hours and relative humidity from 15 meteorological stations was used in the analysis. Results show that: 1) Sensitivity coefficients of wind speed, air temperature and sunshine hours were positive except for those of air tem- perature of Arxan Meteorological Station, while those of relative humidity were all negative. Relative humidity was the most sensitive variable in general for the Tao'er River Basin, followed by sunshine hours, wind speed and air tem- perature. 2) Similar to climate variable, monthly sensitivity coefficients exhibit large annual fluctuations. 3) Sensitivity coefficients for four climate variables all showed significant trends in seasonal/yearly series. Also, sensitivity coefficients of air temperature, sunshine hours and wind speed all showed significant trends in spring. 4) Among all sensitiv- ity coefficients, the average yearly sensitivity coefficient of relative humidity was highest throughout the basin and showed largest spatial variability. Longitudinal distribution of sensitivity coefficients for air temperature, relative hu- midity and sunshine hours was also found, which was similar to the distribution of the three climate variables.

Parametric study on smoothed particle hydrodynamics for accurate determination of drag coefficient for a circular cylinder

Simulations of two-dimensional(2D) flow past a circular cylinder with the smoothed particle hydrodynamics(SPH) method were conducted in order to accurately determine the drag coefficient. The fluid was modeled as a viscous liquid with weak compressibility. Boundary conditions,such as a no-slip solid wall, inflow and outflow, and periodic boundaries, were employed to resemble the physical problem. A sensitivity analysis, which has been rarely addressed in previous studies, was conducted on several SPH parameters. Hence, the effects of distinct parameters, such as the kernel choices and the domain dimensions, were investigated with the goal of obtaining highly accurate results. A range of Reynolds numbers(1-500) was simulated, and the results were compared with existing experimental data. It was observed that the domain dimensions and the resolution of SPH particles, in comparison to the obstacle size, affected the obtained drag coefficient significantly. Other parameters, such as the background pressure, influenced the transient condition, but did not influence the steady state at which the drag coefficient was determined.

Sensitivity Analysis of Parameters in Water Quality Models and Water Environment Management

The impacts of changes of various parameters and stochastic factors on water quality models were studied. The impact of deviation of the degradation coefficient on the model results was investigated. The degradation coefficient was decomposed into the exact part and the deviation part, and the relationship between the errors of the water quality model results and the deviation of the degradation coefficient was derived. The impact of changes in the initial concentration on the model results was discussed. A linear relationship between the initial concentration changes and errors in the model results was obtained, and relevant recommendations to the water quality management were made based on the results. The impacts of stochastic factors in the water environment on the water quality model were analyzed. A variety of random factors which may affect the water quality conditions were attributed to one stochastic factor and it was further assumed to be the white noise. The solutions to the water quality model including the stochastic process were obtained by solving the stochastic differential equation. Simulation results showed that the decay trend of the concentration of the solute would not be changed, and that the results would fluctuate around the expectation centered at each corresponding displacement

Data-driven estimation of joint roughness coefficient

Joint roughness is one of the most important issues in the hydromechanical behavior of rock mass.Therefore,the joint roughness coefficient(JRC)estimation is of paramount importance in geomechanics engineering applications.Studies show that the application of statistical parameters alone may not produce a sufficiently reliable estimation of the JRC values.Therefore,alternative data-driven methods are proposed to assess the JRC values.In this study,Gaussian process(GP),K-star,random forest(RF),and extreme gradient boosting(XGBoost)models are employed,and their performance and accuracy are compared with those of benchmark regression formula(i.e.Z2,Rp,and SDi)for the JRC estimation.To analyze the models’performance,112 rock joint profile datasets having eight common statistical parameters(R_(ave),R_(max),SD_(h),iave,SD_(i),Z_(2),R_(p),and SF)and one output variable(JRC)are utilized,of which 89 and 23 datasets are used for training and validation of models,respectively.The interpretability of the developed XGBoost model is presented in terms of feature importance ranking,partial dependence plots(PDPs),feature interaction,and local interpretable model-agnostic explanations(LIME)techniques.Analyses of results show that machine learning models demonstrate higher accuracy and precision for estimating JRC values compared with the benchmark empirical equations,indicating the generalization ability of the data-driven models in better estimation accuracy.

A Fast Product of Conditional Reduction Method for System Failure Probability Sensitivity Evaluation

Systemreliability sensitivity analysis becomes difficult due to involving the issues of the correlation between failure modes whether using analytic method or numerical simulation methods.A fast conditional reduction method based on conditional probability theory is proposed to solve the sensitivity analysis based on the approximate analytic method.The relevant concepts are introduced to characterize the correlation between failure modes by the reliability index and correlation coefficient,and conditional normal fractile the for the multi-dimensional conditional failure analysis is proposed based on the two-dimensional normal distribution function.Thus the calculation of system failure probability can be represented as a summation of conditional probability terms,which is convenient to be computed by iterative solving sequentially.Further the system sensitivity solution is transformed into the derivation process of the failure probability correlation coefficient of each failure mode.Numerical examples results show that it is feasible to apply the idea of failure mode relevancy to failure probability sensitivity analysis,and it can avoid multi-dimension integral calculation and reduce complexity and difficulty.Compared with the product of conditional marginalmethod,a wider value range of correlation coefficient for reliability analysis is confirmed and an acceptable accuracy can be obtained with less computational cost.

Spatial Identification of Urban Ecological Function on the North Slope of Qinling Mountains Based on Ecological Sensitivity—A Case Study in Baoji, China

Since the 17th National Congress of the Communist Party of China, ecological civilization has been the key construction goal in China, which has a profound impact on the process of urbanization. In recent years, with the rapid development of urbanization and unreasonable land development and utilization, the ecological environment has deteriorated sharply, and the stability of ecological environment has always been a difficult problem in the process of regional development. The spatial division of urban ecological function can be divided into different types of spatial utilization according to the fragile state of ecological environment, which not only guarantees urban construction but also maintains the ecological environment health, and has great economic benefits and ecological value in formulating regional development strategies and ecological protection. In this paper, from four perspectives of “land, water, human and forest”, eight factors affecting ecological sensitivity were selected, and GIS spatial superposition method was used to conduct qualitative and quantitative analysis on the ecological sensitivity of Baoji City, and the evaluation results of single factor ecological sensitivity and comprehensive ecological sensitivity were obtained. The areas with different ecological sensitivity are divided into extremely sensitive areas, highly sensitive areas, moderately sensitive areas, slightly sensitive areas and non-sensitive areas. The research shows that the proportion of extreme, high, moderate, mild and insensitive areas in Baoji City is 7.32%, 10.57%, 22.25%, 42.91% and 16.95% respectively. Finally, the areas with different sensitivity grades are identified as three types of urban ecological function areas: ecological conservation area, ecological coordinated moderate utilization area and ecological suitable construction area, so as to provide scientific theoretical basis for urban construction and land use optimization in Baoji City.

Optimal configuration strategy of energy storage system in high photovoltaic penetration micro-grid based on voltage sensitivity analysis

Energy storage is an effective measure to deal with internal power fluctuation of micro-grid and ensure stable operation, especially in the micro-grid with high photovoltaic(PV) penetration. Its capacity configuration is related to the steady, safety and economy of micro-grid.In order to improve the absorptive capacity of micro-grid on maximizing the use of distributed PV power in micro-grid, and improve the power quality, an optimal energy storage configuration strategy is proposed, which takes many factors into account, such as the topology of micro-grid, the change of irradiance, the load fluctuation and the cable. The strategy can optimize the energy storage allocation model to minimize the storage power capacity and optimize the node configuration.The key electrical nodes are identified by using the sensitivity coefficient of the voltage, and then the model is optimized to simplify calculation. Finally, an example of the European low-voltage micro-grid and a micro-grid system in the laboratory is used to verify the effectiveness of the proposed method.The results show that the proposed method can optimize the allocation of capacity and the node of the energy storage system.

Regularized determination of interfacial heat transfer coefficient during ZL102 solidification process

The interfacial heat transfer coefficient(IHTC)between the casting and the mould is essential to the numerical simulation as one of boundary conditions.A new inverse method was presented according to the Tikhonov regularization theory.A regularized functional was established and the regularization parameter was deduced.The functional was solved to determine the interfacial heat transfer coefficient by using the sensitivity coefficient and Newton-Raphson iteration method.The temperature measurement experiment was done to ZL102 sand mold casting,and the appropriate mathematical model of the IHTC was established.Moreover, the regularization method was used to determinate the IHTC.The results indicate that the regularization method is very efficient in overcoming the ill-posedness of the inverse heat conduction problem(IHCP),and ensuring the accuracy and stability of the solutions.

Sensitivity Analysis of the Penman-Monteith Reference Evapotranspiration to Climatic Variables: Case of Burkina Faso

Sensitivity analysis is important in understanding the effect of each climatic input variable on the variation of the evapotranspiration which is a significant element for hydrological modelling, irrigation programs, and water resources management. This study investigates the responses of evapotranspiration to the variation of maximum and minimum temperature, solar radiation, wind speed and maximum and minimum relative humidity. Daily data from 1998 to 2012 of eight stations are used. For each climatic variable, a variation of 5% up to ±25% was performed in order to evaluate the sensitivity of the evapotranspiration to the input variables. Results show that evapotranspiration is more sensitive to the variation of solar radiation, maximal temperature and wind speed, respectively.

Global Sensitivity Analysis in Physiological Systems

Pharmacokinetic models are mathematical models which provide insights into the interaction of chemicals with biological processes. During recent decades, these models have become central of attention in industry that caused to do a lot of efforts to make them more accurate. Current work studies the process of drug and nanoparticle (NPs) distribution throughout the body which consists of a system of ordinary differential equations. We use a tri-compartmental model to study the perfusion of NPs in tissues and a six-compartmental model to study drug distribution in different body organs. We have performed global sensitivity analysis by LHS Monte Carlo method using PRCC. We identify the key parameters that contribute most significantly to the absorption and distribution of drugs and NPs in different organs in body.

Sensitivity Study on Durability Variables of Marine Concrete Structures

In order to study the influence of parameters on durability of marine concrete structures, the parameter＇s sensitivity analysis was studied in this paper. With the Fick＇s 2nd law of diffusion and the deterministic sensitivity analysis method （DSA）, the sensitivity factors of apparent surface chloride content, apparent chloride diffusion coefficient and its time dependent attenuation factor were analyzed. The results of the analysis show that the impact of design variables on concrete durability was different. The values of sensitivity factor of chloride diffusion coefficient and its time dependent attenuation factor were higher than others. Relative less error in chloride diffusion coefficient and its time dependent attenuation coefficient induces a bigger error in concrete durability design and life prediction. According to probability sensitivity analysis （PSA）, the influence of mean value and variance of concrete durability design variables on the durability failure probability was studied. The results of the study provide quantitative measures of the importance of concrete durability design and life prediction variables. It was concluded that the chloride diffusion coefficient and its time dependent attenuation factor have more influence on the reliability of marine concrete structural durability. In durability design and life prediction of marine concrete structures, it was very important to reduce the measure and statistic error of durability design variables.

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

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