Linearization of Radiative Transfer Equation (RTE) is the key step in physical retrieval of atmospheric temperature and moisture profiles from InfRared (IR) sounder observations. In this paper, the successive forms of...Linearization of Radiative Transfer Equation (RTE) is the key step in physical retrieval of atmospheric temperature and moisture profiles from InfRared (IR) sounder observations. In this paper, the successive forms of temperature and water vapor mixing ratio component weighting functions are derived by applying one term variation method to RTE with surface emissivity and solar reflectivity contained. Retrivals of temperature and water vapor mixing ratio profiles from simulated Atmospheric Infrared Sounder (AIRS) observations with surface emissivity and solar reflectivity are presented.展开更多
A new static microwave sounding unit （MSU） channel 4 weighting function is obtained from using Coupled Model Inter-comparison Project, Phase 5 （CMIP5） historical multimodel simulations as inputs into the fast Radi...A new static microwave sounding unit （MSU） channel 4 weighting function is obtained from using Coupled Model Inter-comparison Project, Phase 5 （CMIP5） historical multimodel simulations as inputs into the fast Radiative Transfer Model for TOVS （RTTOV v10）. For the same CMIP5 model simulations, it is demonstrated that the computed MSU channel 4 brightness temperature （T4） trends in the lower stratosphere over both the globe and the tropics using the proposed weighting function are equivalent to those calculated by RTTOV, but show more cooling than those computed using the traditional UAH （University of Alabama at Huntsville） or RSS （Remote Sensing Systems in Santa Rosa, California） static weighting functions. The new static weighting function not only reduces the computational cost, but also reveals reasons why trends using a radiative transfer model are different from those using a traditional static weighting function. This study also shows that CMIP5 model simulated T4 trends using the traditional UAH or RSS static weighting functions show less cooling than satellite observations over the globe and the tropics. Although not completely removed, this difference can be reduced using the proposed weighting function to some extent, especially over the tropics. This work aims to explore the reasons for the trend differences and to see to what extent they are related to the inaccurate weighting functions. This would also help distinguish other sources for trend errors and thus better understand the climate change in the lower stratosphere.展开更多
The selection and scaling of ground motion records is considered a primary and essential task in performing structural analysis and design.Conventional methods involve using ground motion models and a conditional spec...The selection and scaling of ground motion records is considered a primary and essential task in performing structural analysis and design.Conventional methods involve using ground motion models and a conditional spectrum to select ground motion records based on the target spectrum.This research demonstrates the influence of adopting different weighted factors for various period ranges during matching selected ground motions with the target hazard spectrum.The event data from the Next Generation Attenuation West 2(NGA-West 2)database is used as the basis for ground motion selection,and hazard de-aggregation is conducted to estimate the event parameters of interest,which are then used to construct the target intensity measure(IM).The target IMs are then used to select ground motion records with different weighted vector-valued objective functions.The weights are altered to account for the relative importance of IM in accordance with the structural analysis application of steel moment resisting frame(SMRF)buildings.Instead of an ordinary objective function for the matching spectrum,a novel model is introduced and compared with the conventional cost function.The results indicate that when applying the new cost function for ground motion selection,it places higher demands on structures compared to the conventional cost function.Moreover,submitting more weights to the first-mode period of structures increases engineering demand parameters.Findings demonstrate that weight factors allocated to different period ranges can successfully account for period elongation and higher mode effects.展开更多
The current existing problem of deep learning framework for the detection and segmentation of electrical equipment is dominantly related to low precision.Because of the reliable,safe and easy-to-operate technology pro...The current existing problem of deep learning framework for the detection and segmentation of electrical equipment is dominantly related to low precision.Because of the reliable,safe and easy-to-operate technology provided by deep learning-based video surveillance for unmanned inspection of electrical equipment,this paper uses the bottleneck attention module(BAM)attention mechanism to improve the Solov2 model and proposes a new electrical equipment segmentation mode.Firstly,the BAM attention mechanism is integrated into the feature extraction network to adaptively learn the correlation between feature channels,thereby improving the expression ability of the feature map;secondly,the weighted sum of CrossEntropy Loss and Dice loss is designed as the mask loss to improve the segmentation accuracy and robustness of the model;finally,the non-maximal suppression(NMS)algorithm to better handle the overlap problem in instance segmentation.Experimental results show that the proposed method achieves an average segmentation accuracy of mAP of 80.4% on three types of electrical equipment datasets,including transformers,insulators and voltage transformers,which improve the detection accuracy by more than 5.7% compared with the original Solov2 model.The segmentation model proposed can provide a focusing technical means for the intelligent management of power systems.展开更多
This paper is devoted to studying the existence of solutions for the following logarithmic Schrödinger problem: −div(a(x)∇u)+V(x)u=ulogu2+k(x)| u |q1−2u+h(x)| u |q2−2u, x∈ℝN.(1)We first prove that the correspon...This paper is devoted to studying the existence of solutions for the following logarithmic Schrödinger problem: −div(a(x)∇u)+V(x)u=ulogu2+k(x)| u |q1−2u+h(x)| u |q2−2u, x∈ℝN.(1)We first prove that the corresponding functional I belongs to C1(HV1(ℝN),ℝ). Furthermore, by using the variational method, we prove the existence of a sigh-changing solution to problem (1).展开更多
The meshless method is a new numerical technique presented in recent years.It uses the moving least square(MLS)approximation as a shape function.The smoothness of the MLS approximation is determined by that of the bas...The meshless method is a new numerical technique presented in recent years.It uses the moving least square(MLS)approximation as a shape function.The smoothness of the MLS approximation is determined by that of the basic function and of the weight function,and is mainly determined by that of the weight function.Therefore,the weight function greatly affects the accuracy of results obtained.Different kinds of weight functions,such as the spline function, the Gauss function and so on,are proposed recently by many researchers.In the present work,the features of various weight functions are illustrated through solving elasto-static problems using the local boundary integral equation method.The effect of various weight functions on the accuracy, convergence and stability of results obtained is also discussed.Examples show that the weight function proposed by Zhou Weiyuan and Gauss and the quartic spline weight function are better than the others if parameters c and α in Gauss and exponential weight functions are in the range of reasonable values,respectively,and the higher the smoothness of the weight function,the better the features of the solutions.展开更多
This paper is devoted to studying the commutators of the multilinear singular integral operators with the non-smooth kernels and the weighted Lipschitz functions. Some mapping properties for two types of commutators o...This paper is devoted to studying the commutators of the multilinear singular integral operators with the non-smooth kernels and the weighted Lipschitz functions. Some mapping properties for two types of commutators on the weighted Lebesgue spaces, which extend and generalize some previous results, are obtained.展开更多
An accurate crack surface opening displacement formula for edge cracks in finite bodies has been derived,and was subsequently used to develop wide-range closed-form weight functions for edge cracks. The analytical wei...An accurate crack surface opening displacement formula for edge cracks in finite bodies has been derived,and was subsequently used to develop wide-range closed-form weight functions for edge cracks. The analytical weight function is general and can be easily used to determine accurate stress intensity factors and crack surface opening displacements for arbitrarily loaded edge cracks with high efficiency.Examples have been given for problems of edge crack(s)with a number of typical load conditions for illustration.展开更多
The Bueckner work conjugate integrals are studied for cracks in anisotropic clastic solids.The difficulties in separating Lekhnitskii's two complex arguments involved in the integrals are overcome and explicit fun...The Bueckner work conjugate integrals are studied for cracks in anisotropic clastic solids.The difficulties in separating Lekhnitskii's two complex arguments involved in the integrals are overcome and explicit functional representa- tions of the integrals are given for several typical cases.It is found that the pseudo- orthogonal property of the eigenfunction expansion forms presented previously for isotropic cases,isotropic bimaterials,and orthotropic cases,are proved to be also valid in the present case of anisotropic material.Finally,Some useful path-independent in- tegrals and weight functions are proposed.展开更多
We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applic...We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applications, we also give estimates of the es- sential norms of weighted composition operators between weighted Banach space of analytic functions and Bloch-type spaces.展开更多
Multiresolution analysis of wavelet theory can give an effective way to describe the information at various levels of approximations or different resolutions, based on spline wavelet analysis,so weight function is ort...Multiresolution analysis of wavelet theory can give an effective way to describe the information at various levels of approximations or different resolutions, based on spline wavelet analysis,so weight function is orthonormally projected onto a sequence of closed spline subspaces, and is viewed at various levels of approximations or different resolutions. Now, the useful new way to research weight function is found, and the numerical result is given.展开更多
The equation of stress intensity factors（SIF） of internally pressurized thick-walled cylinder was used as the reference case. SIF equation of rotating thick-walled cylinder containing a radial crack along the intern...The equation of stress intensity factors（SIF） of internally pressurized thick-walled cylinder was used as the reference case. SIF equation of rotating thick-walled cylinder containing a radial crack along the internal bore was presented in weight function method. The weight function formulas were worked out and can be used for all kinds of depth of cracks, rotating speed, material, size of thick-walled cylinder to calculate the stress intensity factors. The results indicated the validity and effectiveness of these formulas. Meanwhile, the rules of the stress intensity factors in rotating thick-walled cylinder with the change of crack depths and the ratio of outer radius to inner radius were studied. The studies are valuable to engineering application.展开更多
In this report the combined method of correlation radar signal(RS)processing based on the theory of atomic functions(AF)is examined.Examples of using of new Kravchenko probability weight functions(WF)designs are prese...In this report the combined method of correlation radar signal(RS)processing based on the theory of atomic functions(AF)is examined.Examples of using of new Kravchenko probability weight functions(WF)designs are presented.Quality functional to estimate accuracy and efficiency of RS processing for concrete physical models is constructed.It is shown that the proposed approach significantly improves the quality of the coherent analysis of RS.展开更多
In this article, we provide estimates for the degree of V bilipschitz determinacy of weighted homogeneous function germs defined on weighted homogeneous analytic variety V satisfying a convenient Lojasiewicz condition...In this article, we provide estimates for the degree of V bilipschitz determinacy of weighted homogeneous function germs defined on weighted homogeneous analytic variety V satisfying a convenient Lojasiewicz condition.The result gives an explicit order such that the geometrical structure of a weighted homogeneous polynomial function germs is preserved after higher order perturbations.展开更多
A numerical solution of the weight function for a two-electrode electromagnetic flowmeter was proposed. The solution was obtained by using the finite element method based on the basic equation of a traditional two-ele...A numerical solution of the weight function for a two-electrode electromagnetic flowmeter was proposed. The solution was obtained by using the finite element method based on the basic equation of a traditional two-electrode electromagnetic flowmeter. The two-dimensional distribution of the weight function of the electromagnetic flowmeter obtained was verified by the analytical solution. Three-dimensional distribution of the weight function was also presented in the paper. It can be employed to analyze the sensitivity and linearity of the electromagnetic flowmeter with non-uniform magnetic field, and even to assist the design of the excitation coil pair.展开更多
Bueckner's work conjugate integral customarily adopted for linear elastic materials is established for an interface crack in dissimilar anisotropic materials.The difficulties in separating Stroh's six complex ...Bueckner's work conjugate integral customarily adopted for linear elastic materials is established for an interface crack in dissimilar anisotropic materials.The difficulties in separating Stroh's six complex arguments involved in the integral for the dissimilar materials are overcome and thert the explicit function representations of the integral are given and studied in detail.It is found that the pseudo-orthogonal properties of the eigenfunction expansion form(EEF)for a crack presented previously in isotropic elastic cases,in isotopic bimaterial cases,and in orthotropic cases are also valid in the present dissimilar arbitrary anisotropic cases.The relation between Bueckner's work conjugate integral and the J-integral in these cases is obtained by introducing a complementary stress- displacement state.Finally,some useful path-independent integrals and weight functions are proposed for calculating the crack tip parameters such as the stress intensity factors.展开更多
A new and simple method is developed to establish the pseudo orthogonal properties (POP) of the eigenfunction expansion form (EEF) of crack-tip stress complex potential functions for cracked anisotropic an...A new and simple method is developed to establish the pseudo orthogonal properties (POP) of the eigenfunction expansion form (EEF) of crack-tip stress complex potential functions for cracked anisotropic and piezoelectric materials, respectively. Di?erent from previous research, the complex argument separation technique is not required so that cumbersome manipulations are avoided. Moreover, it is shown, di?erent from the previous research too, that the orthogonal properties of the material characteristic matrices A and B are no longer necessary in obtaining the POP of EEF in cracked piezoelectric materials. Of the greatest signi?cance is that the method presented in this paper can be widely extended to treat many kinds of problems concerning path- independent integrals with multi-variables.展开更多
Two computational cases that have analytic solutions are employed for studying the adaptive grid tech-nique based on the variational principle. The results show that for the computational case of traveling shock waves...Two computational cases that have analytic solutions are employed for studying the adaptive grid tech-nique based on the variational principle. The results show that for the computational case of traveling shock waves the weight function, with the 2nd-order derivation terms taken into consideration, can more effectively reduce the error than one with gradient terms. For the case of cyclonic frontogenesis, weight func-tions only related to the gradient are unable to enhance the computational accuracy while ones with the wind field and frontogenesis function taken into consideration can more reasonably arrange the grid. Com-pared with analytic solutions, the adaptive grid technique suggested in this paper can improve computational accuracy and it displays the prominent advantage of saving memory.展开更多
文摘Linearization of Radiative Transfer Equation (RTE) is the key step in physical retrieval of atmospheric temperature and moisture profiles from InfRared (IR) sounder observations. In this paper, the successive forms of temperature and water vapor mixing ratio component weighting functions are derived by applying one term variation method to RTE with surface emissivity and solar reflectivity contained. Retrivals of temperature and water vapor mixing ratio profiles from simulated Atmospheric Infrared Sounder (AIRS) observations with surface emissivity and solar reflectivity are presented.
基金supported by the National Program on Key Basic Research Projects of China(Grant Nos.2010CB951604 and 2010CB28402)
文摘A new static microwave sounding unit （MSU） channel 4 weighting function is obtained from using Coupled Model Inter-comparison Project, Phase 5 （CMIP5） historical multimodel simulations as inputs into the fast Radiative Transfer Model for TOVS （RTTOV v10）. For the same CMIP5 model simulations, it is demonstrated that the computed MSU channel 4 brightness temperature （T4） trends in the lower stratosphere over both the globe and the tropics using the proposed weighting function are equivalent to those calculated by RTTOV, but show more cooling than those computed using the traditional UAH （University of Alabama at Huntsville） or RSS （Remote Sensing Systems in Santa Rosa, California） static weighting functions. The new static weighting function not only reduces the computational cost, but also reveals reasons why trends using a radiative transfer model are different from those using a traditional static weighting function. This study also shows that CMIP5 model simulated T4 trends using the traditional UAH or RSS static weighting functions show less cooling than satellite observations over the globe and the tropics. Although not completely removed, this difference can be reduced using the proposed weighting function to some extent, especially over the tropics. This work aims to explore the reasons for the trend differences and to see to what extent they are related to the inaccurate weighting functions. This would also help distinguish other sources for trend errors and thus better understand the climate change in the lower stratosphere.
基金financial support from Teesside University to support the Ph.D. program of the first author.
文摘The selection and scaling of ground motion records is considered a primary and essential task in performing structural analysis and design.Conventional methods involve using ground motion models and a conditional spectrum to select ground motion records based on the target spectrum.This research demonstrates the influence of adopting different weighted factors for various period ranges during matching selected ground motions with the target hazard spectrum.The event data from the Next Generation Attenuation West 2(NGA-West 2)database is used as the basis for ground motion selection,and hazard de-aggregation is conducted to estimate the event parameters of interest,which are then used to construct the target intensity measure(IM).The target IMs are then used to select ground motion records with different weighted vector-valued objective functions.The weights are altered to account for the relative importance of IM in accordance with the structural analysis application of steel moment resisting frame(SMRF)buildings.Instead of an ordinary objective function for the matching spectrum,a novel model is introduced and compared with the conventional cost function.The results indicate that when applying the new cost function for ground motion selection,it places higher demands on structures compared to the conventional cost function.Moreover,submitting more weights to the first-mode period of structures increases engineering demand parameters.Findings demonstrate that weight factors allocated to different period ranges can successfully account for period elongation and higher mode effects.
基金Jilin Science and Technology Development Plan Project(No.20200403075SF)Doctoral Research Start-Up Fund of Northeast Electric Power University(No.BSJXM-2018202).
文摘The current existing problem of deep learning framework for the detection and segmentation of electrical equipment is dominantly related to low precision.Because of the reliable,safe and easy-to-operate technology provided by deep learning-based video surveillance for unmanned inspection of electrical equipment,this paper uses the bottleneck attention module(BAM)attention mechanism to improve the Solov2 model and proposes a new electrical equipment segmentation mode.Firstly,the BAM attention mechanism is integrated into the feature extraction network to adaptively learn the correlation between feature channels,thereby improving the expression ability of the feature map;secondly,the weighted sum of CrossEntropy Loss and Dice loss is designed as the mask loss to improve the segmentation accuracy and robustness of the model;finally,the non-maximal suppression(NMS)algorithm to better handle the overlap problem in instance segmentation.Experimental results show that the proposed method achieves an average segmentation accuracy of mAP of 80.4% on three types of electrical equipment datasets,including transformers,insulators and voltage transformers,which improve the detection accuracy by more than 5.7% compared with the original Solov2 model.The segmentation model proposed can provide a focusing technical means for the intelligent management of power systems.
文摘This paper is devoted to studying the existence of solutions for the following logarithmic Schrödinger problem: −div(a(x)∇u)+V(x)u=ulogu2+k(x)| u |q1−2u+h(x)| u |q2−2u, x∈ℝN.(1)We first prove that the corresponding functional I belongs to C1(HV1(ℝN),ℝ). Furthermore, by using the variational method, we prove the existence of a sigh-changing solution to problem (1).
文摘The meshless method is a new numerical technique presented in recent years.It uses the moving least square(MLS)approximation as a shape function.The smoothness of the MLS approximation is determined by that of the basic function and of the weight function,and is mainly determined by that of the weight function.Therefore,the weight function greatly affects the accuracy of results obtained.Different kinds of weight functions,such as the spline function, the Gauss function and so on,are proposed recently by many researchers.In the present work,the features of various weight functions are illustrated through solving elasto-static problems using the local boundary integral equation method.The effect of various weight functions on the accuracy, convergence and stability of results obtained is also discussed.Examples show that the weight function proposed by Zhou Weiyuan and Gauss and the quartic spline weight function are better than the others if parameters c and α in Gauss and exponential weight functions are in the range of reasonable values,respectively,and the higher the smoothness of the weight function,the better the features of the solutions.
基金Supported by the National Natural Science Foundation of China (10771054,11071200)the NFS of Fujian Province of China (No. 2010J01013)
文摘This paper is devoted to studying the commutators of the multilinear singular integral operators with the non-smooth kernels and the weighted Lipschitz functions. Some mapping properties for two types of commutators on the weighted Lebesgue spaces, which extend and generalize some previous results, are obtained.
文摘An accurate crack surface opening displacement formula for edge cracks in finite bodies has been derived,and was subsequently used to develop wide-range closed-form weight functions for edge cracks. The analytical weight function is general and can be easily used to determine accurate stress intensity factors and crack surface opening displacements for arbitrarily loaded edge cracks with high efficiency.Examples have been given for problems of edge crack(s)with a number of typical load conditions for illustration.
基金The project supported by the National Natural Science Foundation of China(19891180)Doctorate Foundation of Xi'an Jiaotong University
文摘The Bueckner work conjugate integrals are studied for cracks in anisotropic clastic solids.The difficulties in separating Lekhnitskii's two complex arguments involved in the integrals are overcome and explicit functional representa- tions of the integrals are given for several typical cases.It is found that the pseudo- orthogonal property of the eigenfunction expansion forms presented previously for isotropic cases,isotropic bimaterials,and orthotropic cases,are proved to be also valid in the present case of anisotropic material.Finally,Some useful path-independent in- tegrals and weight functions are proposed.
文摘We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applications, we also give estimates of the es- sential norms of weighted composition operators between weighted Banach space of analytic functions and Bloch-type spaces.
基金theNationalNaturalScienceFoundationofChina (No .50 40 90 0 8)
文摘Multiresolution analysis of wavelet theory can give an effective way to describe the information at various levels of approximations or different resolutions, based on spline wavelet analysis,so weight function is orthonormally projected onto a sequence of closed spline subspaces, and is viewed at various levels of approximations or different resolutions. Now, the useful new way to research weight function is found, and the numerical result is given.
文摘The equation of stress intensity factors（SIF） of internally pressurized thick-walled cylinder was used as the reference case. SIF equation of rotating thick-walled cylinder containing a radial crack along the internal bore was presented in weight function method. The weight function formulas were worked out and can be used for all kinds of depth of cracks, rotating speed, material, size of thick-walled cylinder to calculate the stress intensity factors. The results indicated the validity and effectiveness of these formulas. Meanwhile, the rules of the stress intensity factors in rotating thick-walled cylinder with the change of crack depths and the ratio of outer radius to inner radius were studied. The studies are valuable to engineering application.
基金Russian Foundation for Basic Research(No.12-02-90425)
文摘In this report the combined method of correlation radar signal(RS)processing based on the theory of atomic functions(AF)is examined.Examples of using of new Kravchenko probability weight functions(WF)designs are presented.Quality functional to estimate accuracy and efficiency of RS processing for concrete physical models is constructed.It is shown that the proposed approach significantly improves the quality of the coherent analysis of RS.
基金Supported by the National Nature Science Foundation of China(10671009,60534080,10871149)
文摘In this article, we provide estimates for the degree of V bilipschitz determinacy of weighted homogeneous function germs defined on weighted homogeneous analytic variety V satisfying a convenient Lojasiewicz condition.The result gives an explicit order such that the geometrical structure of a weighted homogeneous polynomial function germs is preserved after higher order perturbations.
基金Supported by Chinese National Programs for High Technology Research and Development(2008AA042207)
文摘A numerical solution of the weight function for a two-electrode electromagnetic flowmeter was proposed. The solution was obtained by using the finite element method based on the basic equation of a traditional two-electrode electromagnetic flowmeter. The two-dimensional distribution of the weight function of the electromagnetic flowmeter obtained was verified by the analytical solution. Three-dimensional distribution of the weight function was also presented in the paper. It can be employed to analyze the sensitivity and linearity of the electromagnetic flowmeter with non-uniform magnetic field, and even to assist the design of the excitation coil pair.
基金The project supported by the National Natural Science Foundation of China and the Graduate School of Xi'an Jiaotong University
文摘Bueckner's work conjugate integral customarily adopted for linear elastic materials is established for an interface crack in dissimilar anisotropic materials.The difficulties in separating Stroh's six complex arguments involved in the integral for the dissimilar materials are overcome and thert the explicit function representations of the integral are given and studied in detail.It is found that the pseudo-orthogonal properties of the eigenfunction expansion form(EEF)for a crack presented previously in isotropic elastic cases,in isotopic bimaterial cases,and in orthotropic cases are also valid in the present dissimilar arbitrary anisotropic cases.The relation between Bueckner's work conjugate integral and the J-integral in these cases is obtained by introducing a complementary stress- displacement state.Finally,some useful path-independent integrals and weight functions are proposed for calculating the crack tip parameters such as the stress intensity factors.
基金Project supported by the Natural Science Foundation of Shaanxi Province (No.2002A18) and the Doctorate Foundation of Xi’an Jiao-Tong University.
文摘A new and simple method is developed to establish the pseudo orthogonal properties (POP) of the eigenfunction expansion form (EEF) of crack-tip stress complex potential functions for cracked anisotropic and piezoelectric materials, respectively. Di?erent from previous research, the complex argument separation technique is not required so that cumbersome manipulations are avoided. Moreover, it is shown, di?erent from the previous research too, that the orthogonal properties of the material characteristic matrices A and B are no longer necessary in obtaining the POP of EEF in cracked piezoelectric materials. Of the greatest signi?cance is that the method presented in this paper can be widely extended to treat many kinds of problems concerning path- independent integrals with multi-variables.
基金Acknowledgments. The research report has been supported jointly by the National Natural Science Foundation of China under Grant Nos.40075024 and 49945009, and by the National Key Basic Research and Development Proj-ect under Grant No. G1998040911.
文摘Two computational cases that have analytic solutions are employed for studying the adaptive grid tech-nique based on the variational principle. The results show that for the computational case of traveling shock waves the weight function, with the 2nd-order derivation terms taken into consideration, can more effectively reduce the error than one with gradient terms. For the case of cyclonic frontogenesis, weight func-tions only related to the gradient are unable to enhance the computational accuracy while ones with the wind field and frontogenesis function taken into consideration can more reasonably arrange the grid. Com-pared with analytic solutions, the adaptive grid technique suggested in this paper can improve computational accuracy and it displays the prominent advantage of saving memory.
