CN115374682B - Space-time collaborative high-precision curved surface modeling method and system - Google Patents
Space-time collaborative high-precision curved surface modeling method and system Download PDFInfo
- Publication number
- CN115374682B CN115374682B CN202211306422.2A CN202211306422A CN115374682B CN 115374682 B CN115374682 B CN 115374682B CN 202211306422 A CN202211306422 A CN 202211306422A CN 115374682 B CN115374682 B CN 115374682B
- Authority
- CN
- China
- Prior art keywords
- curved surface
- ecological environment
- time
- equation set
- environment element
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02A—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
- Y02A90/00—Technologies having an indirect contribution to adaptation to climate change
- Y02A90/10—Information and communication technologies [ICT] supporting adaptation to climate change, e.g. for weather forecasting or climate simulation
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Mathematical Physics (AREA)
- Mathematical Optimization (AREA)
- Data Mining & Analysis (AREA)
- General Engineering & Computer Science (AREA)
- Computational Mathematics (AREA)
- Mathematical Analysis (AREA)
- Pure & Applied Mathematics (AREA)
- Computer Hardware Design (AREA)
- Operations Research (AREA)
- Evolutionary Computation (AREA)
- Algebra (AREA)
- Geometry (AREA)
- Databases & Information Systems (AREA)
- Software Systems (AREA)
- Processing Or Creating Images (AREA)
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
Abstract
The application relates to the technical field of electric digital data processing, and provides a space-time collaborative high-precision curved surface modeling method and system. The method bagComprises the following steps: to pairtPerforming finite difference dispersion on a partial differential equation set of the ecological environment element curved surface of the moment target area to obtain a first dispersion equation set; for points in the target area（x，y）Over time in the environmenttCarrying out finite difference dispersion on the partial differential equation set of the change curve to obtain a second dispersion equation set; determining a high-precision curved surface modeling finite difference equation set of space-time coordination based on the first discrete equation set and the second discrete equation set; and inputting the observation data of the ecological environment element to be simulated, which is acquired in advance, in the target area and the initial curved surface of the ecological environment element to be simulated, which is acquired in advance, into the space-time cooperative high-precision curved surface modeling finite difference equation set for iterative solution to obtain an ecological environment element simulation result, so that the precision of the ecological environment element simulation result is improved.
Description
Technical Field
The application relates to the technical field of electric digital data processing, in particular to a space-time collaborative high-precision curved surface modeling method and system.
Background
Ecological environment factors, such as temperature, precipitation, carbon dioxide concentration, etc., are the natural basis on which the human society lives and develops. The scientific understanding of the basic spatial distribution and change rules of these ecological environment elements is the primary task of ecological environment informatics. In order to express and analyze the ecological environment elements more accurately, the gridding expression of the ecological environment elements can be abstracted into mathematical 'curved surfaces', and then the mathematical 'curved surfaces' are simulated through a curved surface modeling technology to obtain spatially continuous ecological environment element curved surfaces.
Based on this, the national scholars Yue Tianxiang team organically combines the system theory, the Surface theory and the optimization control theory, and provides a High-precision Surface Modeling method (HASM for short), and through years of development, HASM has become an important mathematical model in the field of ecological environment element simulation, and is widely applied in the fields of climate, soil, ecology and the like.
The HASM combines macroscopic information and details to perform high-precision ecological environment element curved surface modeling, and solves the problem of errors in the modeling process. However, the earth surface system and its ecological environment elements are often dynamically changed, such as the earth climate system, the state of which changes every moment, and the climate elements, such as air temperature, relative humidity, etc., are not only closely related in space, but also strongly related in time, if they are simulated according to the conventional HASM, only the spatial correlation of the ecological environment elements is considered, and the inherent temporal correlation is broken, so that the spatiotemporal correlation between the data cannot be reflected, resulting in insufficient precision of the simulation result.
Therefore, there is a need to provide an improved solution to the above-mentioned deficiencies of the prior art.
Disclosure of Invention
The present application aims to provide a method and a system for modeling a space-time collaborative high-precision curved surface, so as to solve or alleviate the above-mentioned problems in the prior art.
In order to achieve the above purpose, the present application provides the following technical solutions:
the application provides a space-time collaborative high-precision curved surface modeling method, which comprises the following steps:
to pairtPerforming finite difference dispersion on a partial differential equation set of the ecological environment element curved surface of the moment target area to obtain a first dispersion equation set;
for points in the target area（x，y）Over time in the environmenttCarrying out finite difference dispersion on the partial differential equation set of the change curve to obtain a second dispersion equation set;
determining a high-precision curved surface modeling finite difference equation set of space-time coordination based on the first discrete equation set and the second discrete equation set;
inputting observation data of the ecological environment elements to be simulated, which are acquired in advance, in the target area and the initial curved surfaces of the ecological environment elements to be simulated, which are acquired in advance, into the space-time cooperative high-precision curved surface modeling finite difference equation set for iterative solution to obtain an ecological environment element simulation result; the observation data is time sequence observation data in a time period to be simulated; the initial curved surface is an ecological environment element curved surface at the initial moment of the time period to be simulated.
Preferably, thetThe partial differential equation set of the ecological environment element curved surface of the time target area is as follows:
wherein:
，
，
，
，
in the formula (I), the compound is shown in the specification,fis the curved surface of the ecological environment element;f（x，y）is a point（x，y）Simulating the value of the ecological environment element;xis the geographical abscissa of the point or points,yis the geographic ordinate of the point;f x is composed offIn thatxA first partial derivative of the direction;f y is composed offIn thatyA first partial derivative of direction;f xx is composed offIn thatxSecond partial derivatives of direction;f yy is composed offIn thatySecond partial derivatives of direction;E、F、Ga first type basic quantity of the curved surface of the ecological environment element;E x is composed ofEIn thatxA first partial derivative of direction;E y is composed ofEIn thatyA first partial derivative of the direction;F x is composed ofFIn thatxA first partial derivative of the direction;F y is composed ofFIn thatyA first partial derivative of the direction;G x is composed ofGIn thatxA first partial derivative of the direction;G y is composed ofGIn thatyA first partial derivative of the direction;L、M、Nthe second kind of basic quantity is the curved surface of the ecological environment element;
the second class of Criserverer symbols is the curved surface of the ecological environment element.
Preferably, the first set of discrete equations comprisestTime point（x，y）The simulation values of the elements in the ecological environment are respectivelyx、 yA first order finite difference equation in direction, and,ttime point（x，y）The simulation value of the ecological environment element isx、yA second order finite difference equation in direction.
Preferably, points within said target area（x，y）Over time in the environmenttThe partial differential equation of the change curve is:
wherein the content of the first and second substances,
，
，
，
，
，
vindicating points（x，y）Over time in the environmenttA change curve;v t to representvIn thattA first partial derivative of the direction;v tt to representvIn thattSecond partial derivatives of direction;
indicating points（x，y）Over time in the environmenttA first base quantity of the profile;
indicating points（x，y）Over time in the environmenttA second base quantity of the profile;
indicating points（x，y）By treating the elements of the ecological environment over timetThe second class of Criserverer symbols of the variation curves.
Preferably, the second set of discrete equations comprises points within the target region（x，y）The simulation value of the ecological environment elements istFirst order finite difference equation in direction, and, points within the target region（x，y）The simulation value of the ecological environment element istSecond order finite difference equations in direction.
Preferably, the high-precision curved surface modeling finite difference equation system of the space-time coordination is as follows:
the initial conditions of the space-time collaborative high-precision curved surface modeling finite difference equation set are as follows:
in the formula (I), the compound is shown in the specification,nrepresenting the number of iterations;trepresents time;i、jrespectively is the row and column coordinates of grid points on the curved surface of the ecological environment element;xis the geographical abscissa of the point or points,yis the geographic ordinate of the point;Δxrepresenting ecological environment elements on the curved surfacexThe iteration step in the direction;Δyrepresenting ecological environment elements on the curved surfaceyThe iteration step in the direction;
to representtGrid point on curved surface of time ecological environment element（i，j）To get it atnThe value of the secondary iteration;
、
、
、
are respectively astGrid point on curved surface of time ecological environment element（i，j）To
To (1) anThe value of the secondary iteration;
a second class of Criserverer symbols which are ecological environment element curved surfaces;
is composed oftGrid point on curved surface of time ecological environment element（i，j）To the second basic quantityLTo (1) anThe value of the secondary iteration;
、
are respectively astGrid point on curved surface of time ecological environment element（i，j）To basic quantity of the first kindE、GTo (1) anThe value of the secondary iteration;Δtrepresents a time step;
indicating points（x，y）Over time in the environmenttThe second class of Criserverer symbols of the variation curves.
Preferably, the observation data of the ecological environment element to be simulated, which is acquired in advance in the target area, and the initial curved surface of the ecological environment element to be simulated, which is acquired in advance, are input into the space-time cooperative high-precision curved surface modeling finite difference equation set for iterative solution, so as to obtain an ecological environment element simulation result, specifically:
inputting the initial curved surface of the ecological environment element to be simulated and observation data of the ecological environment element to be simulated corresponding to the initial time of the simulation time period into a traditional high-precision curved surface modeling equation set for curved surface simulation to obtain an iteration initial value;
and inputting the iteration initial value to the space-time cooperative high-precision curved surface modeling finite difference equation set according to a preset time step for iterative solution to obtain a time sequence of ecological environment element simulation results.
Preferably, the iterative solution is performed by converting the space-time collaborative high-precision curved surface modeling finite difference equation set into a constrained least square problem, the expression of which is as follows:
in the formula (I), the compound is shown in the specification,nrepresenting the number of iterations;
to representtThe first grid point of each grid point on the curved surface of the time ecological environment elementnThe value of the secondary iteration;
，trepresents time;
is thattDiscrete points on curved surface of time ecological environment element（i，j）The first of the simulation values of the ecological environment elementsnThe value of the sub-iteration is,nis a positive integer and is a non-zero integer,tis an integer greater than 0;i、jrespectively the row and column coordinates of grid points on the curved surface of the ecological environment element;I、Jthe number of rows and columns of discrete grid points on the curved surface of the ecological environment element;AandBmodeling coefficient terms of a finite difference equation set for the high-precision curved surface of the time-space coordination;
and
modeling a right-end term of a finite difference equation set for the high-precision curved surface of the time-space coordination;Sa sampling matrix constructed according to sampling points;krepresenting a sample vector.
Preferably, the space-time collaborative high-precision curved surface modeling finite difference equation set is converted into a linear least square problem by adopting a lagrangian factor method, wherein the expression of the linear least square problem is as follows:
in the formula (I), the compound is shown in the specification,
，
is thattDiscrete points on curved surface of time ecological environment element（i，j）The first of the simulation values of the ecological environment elementsnA secondary iteration value;trepresents time;AandBmodeling coefficient terms of a finite difference equation set for the high-precision curved surface of the time-space coordination;
and
modeling a right-end term of a finite difference equation set for the high-precision curved surface of the time-space coordination;Sa sampling matrix constructed according to sampling points;krepresenting a sampling vector;λis a preset real number.
The embodiment of the present application further provides a space-time collaborative high-precision curved surface modeling system, including:
a first discrete unit configured as a pairtPerforming finite difference dispersion on a partial differential equation set of the ecological environment element curved surface of the moment target area to obtain a first dispersion equation set;
a second discrete unit configured to pair points in the target region（x，y）By treating the elements of the ecological environment over timetCarrying out finite difference dispersion on the partial differential equation set of the change curve to obtain a second discrete equation set;
the joint unit is configured to determine a high-precision curved surface modeling finite difference equation set based on the first discrete equation set and the second discrete equation set;
the solving unit is configured to input observation data of the ecological environment elements to be simulated, which are acquired in advance, in the target area and initial curved surfaces of the ecological environment elements to be simulated, which are acquired in advance, into the space-time cooperative high-precision curved surface modeling finite difference equation set for iterative solution to obtain an ecological environment element simulation result; the observation data is time sequence observation data in a time period to be simulated; the initial curved surface is an ecological environment element curved surface at the initial moment of the time period to be simulated.
Has the advantages that:
in the technical scheme of the application, thetPerforming finite difference dispersion on a partial differential equation set of the ecological environment element curved surface of the moment target area to obtain a first discrete equation set; for points in the target area（x，y）Over time in the environmenttCarrying out finite difference dispersion on the partial differential equation set of the change curve to obtain a second dispersion equation set; determining a high-precision curved surface modeling finite difference equation set of space-time coordination based on the first discrete equation set and the second discrete equation set; and inputting the observation data of the ecological environment element to be simulated, which is acquired in advance, in the target area and the initial curved surface of the ecological environment element to be simulated, which is acquired in advance, into a space-time cooperative high-precision curved surface modeling finite difference equation set for iterative solution to obtain an ecological environment element simulation result. When the ecological environment element is simulated, the method provided by the steps not only considers the spatial correlation, but also sufficiently combines the inherent time dimension information, thereby improving the precision of the simulation result of the ecological environment element.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, are included to provide a further understanding of the application, and the description of the exemplary embodiments and illustrations of the application are intended to explain the application and are not intended to limit the application. Wherein:
FIG. 1 is a schematic flow diagram of a spatiotemporal collaborative high precision surface modeling method provided in accordance with some embodiments of the present application;
FIG. 2 is a logic diagram of a spatiotemporal collaborative high precision surface modeling method provided in accordance with some embodiments of the present application;
fig. 3 is a graph illustrating error comparison of simulation results of a conventional HASM and HASM-ST provided according to some embodiments of the present application;
fig. 4 is a graph illustrating correlation of simulation results of conventional HASMs and HASM-ST with observed data according to some embodiments of the present application;
FIG. 5 is a schematic diagram of a spatiotemporal collaborative high-precision surface modeling system provided in accordance with some embodiments of the present application.
Detailed Description
The present application will be described in detail below with reference to the embodiments with reference to the attached drawings. The various examples are provided by way of explanation of the application and are not limiting of the application. In fact, it will be apparent to those skilled in the art that modifications and variations can be made in the present application without departing from the scope or spirit of the application. For instance, features illustrated or described as part of one embodiment, can be used with another embodiment to yield a still further embodiment. It is therefore intended that the present application cover the modifications and variations of this invention provided they come within the scope of the appended claims and their equivalents.
In the following description, references to the terms "first/second/third" are only to distinguish similar objects and do not denote a particular order, but rather "first/second/third" may, where permissible, be interchanged with a particular order or sequence so that the embodiments of the present application described herein may be practiced other than as specifically illustrated or described herein.
Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs. The terminology used herein is for the purpose of describing embodiments of the disclosure only and is not intended to be limiting of the disclosure.
Exemplary method
The embodiment of the application provides a space-time collaborative high-precision curve modeling method, as shown in fig. 1-4, the method comprises the following steps:
step S101, pairtCarrying out finite difference dispersion on partial differential equation set of ecological environment element curved surface of the time target area to obtain a first dispersion squareAnd (5) program grouping.
It should be understood that the curved surface of the ecological environment element is one of the important concepts of the concept system of the scientific policy platform (IPBES) between biodiversity and the government of ecosystem service in united nations, that is, the earth surface system and the ecological environment element thereof are classified according to the contribution of the natural system and the natural system to human beings and the driving force of the change of the natural system, and the curved surface of the natural system, the driving force of the change of the natural system and the curved surface of the contribution of the natural system to human beings are collectively referred to as the curved surface of the ecological environment element.
In the embodiment of the application, the curved surface of the ecological environment element is a simulated curved surface of the ecological environment element in the target area, which is established based on an integrated system theory, a curved surface theory and an optimal control theory, and is determined by a first basic quantity and a second basic quantity together and uniquely according to a basic law of the curved surface theory, wherein the first basic quantity isE、F、GExpressing the detail information observed above the earth's surface, a second fundamental quantityL、M、NExpressing macroscopic information observed outside the earth's surface. Then, based on the theorem of theory of surfaces, a first basic quantity is setE、F、GAnd a second basic quantityL、M、NThe symmetry is satisfied,E、F、Gthe positive and the negative are determined,L、M、Nsatisfy the system of Gauss equations, i.e.tThe time ecological environment element curved surface can be expressed by the following partial differential equation system:
wherein:
，
，
，
，
in the formula (I), the compound is shown in the specification,fis a curved surface of the element of the ecological environment,f（x，y）is a point（x，y）Simulating the value of the ecological environment element;xis the geographical abscissa of the point or points,yis the geographic ordinate of the point;f x is composed offIn thatxA first partial derivative of the direction;f y is composed offIn thatyA first partial derivative of the direction;f xx is composed offIn thatxSecond partial derivatives of direction;f yy is composed offIn thatySecond partial derivatives of direction;E、F、Ga first type basic quantity of the curved surface of the ecological environment element;E x is composed ofEIn thatxA first partial derivative of the direction;E y is composed ofEIn thatyA first partial derivative of the direction;F x is composed ofFIn thatxA first partial derivative of the direction;F y is composed ofFIn thatyA first partial derivative of the direction;G x is composed ofGIn thatxA first partial derivative of the direction;G y is composed ofGIn thatyFirst order partial derivatives of directionCounting;L、M、Na second type basic quantity of the curved surface of the ecological environment element;
the second class of Criserverer symbols is the curved surface of the ecological environment element.
Given the initial conditions:f（x，y）=f（x 0 ，y 0 ）（x=x 0 ，y=y 0 ）then, the partial differential equation system of the curved surface of the ecological environment element expressed by the formula (1) has unique solutionz=f（x，y）。
In order to solve the partial differential equation system of the curved surface of the ecological environment element, finite difference discretization is needed, namely, the target area space discretization is carried out in the form of grid points, and the process is as follows: the target area is converted to 0,L x ]×[0，L y ]dimensionless standardized computation domainsΩWherein, in the step (A),L x 、L y are respectively a computational domainΩInxLength in direction andythe length of the direction. For computing domainΩPerforming orthogonal subdivision to obtain spatial discretizationI×JA computational grid ofiGo to the firstjFor computational grids of columns｛（x i ，y j ）｝Is shown to bex、yThe step size in the direction is:
and constructing the discrete grid of the partial differential equation set of the ecological environment element curved surface by taking the central point of the computational grid as a computational node. Is provided withf（x，y，t）Is composed oftTime point（x，y）The numerical solution (i.e. the simulation value of the ecological environment element) of (A) is based on the finite difference method for the first basic quantity、Second basic quantity、And carrying out numerical value dispersion on the partial differential equation set of the ecological environment element curved surface to obtain a first discrete equation set, wherein the first discrete equation set comprisestTime point（x，y）The simulation values of the elements in the ecological environment are respectivelyx、yA first order finite difference equation in direction, and,ttime point（x，y）The simulation value of the ecological environment element isx、yA second order finite difference equation in direction.
Wherein the content of the first and second substances,ttime point（x，y）The simulation values of the elements in the ecological environment are respectivelyx、yThe first order finite difference equation in direction is as follows:
in the formula (I), the compound is shown in the specification,f x （x，y，t）is composed oftTime point（x，y）The simulation value of the ecological environment element isxThe first order finite difference in direction is,f y （x，y，t）is composed oftTime point（x，y）The simulation value of the ecological environment factors isxFirst order finite difference in direction.
tTime point（x，y）The simulation value of the ecological environment element isx、yThe second order finite difference equation in direction is as follows:
in the formula (I), the compound is shown in the specification,f xx （x，y，t）is composed oftTime point（x，y）The simulation value of the ecological environment element isxThe second order finite difference in direction is,f yy （x，y，t）is composed oftTime point（x，y）The simulation value of the ecological environment element isxSecond order finite difference in direction.
Step S102, aiming at points in the target area（x，y）Over time in the environmenttAnd carrying out finite difference dispersion on the partial differential equation set of the change curve to obtain a second discrete equation set.
Points in the target area in consideration of time-varying characteristics of the ecological environment elements（x，y）Ecological environmentEnvironmental factors over timetThe variation curve can be expressed as:
then the point in the target area（x，y）Over time in the environmenttThe system of partial differential equations for the variation curve is expressed as:
（6）
wherein the content of the first and second substances,
，
，
，
，
，
vindicating points（x，y）Over time in the environmenttA variation curve;v t to representvIn thattA first partial derivative of the direction;v tt to representvIn thattSecond partial derivatives of direction;
indicating points（x，y）Over time in the environmenttA first base quantity of the profile;
indicating points（x，y）Over time in the environmenttA second base quantity of the profile;
indicating points（x，y）Over time in the environmenttThe second class of Criserverer symbols of the variation curves.
To solve for points in the target area（x，y）Over time in the environmenttThe partial differential equation system of the change curve also needs to carry out finite difference dispersion on the time, namely, the time period to be simulated is dispersed into a time point form, and the process is as follows: the time period to be simulated is converted to 0,L t ]dimensionless standardized computation domainsΩ’Wherein, in the process,L t calculating the total length of the time period to be simulatedΩ’Is divided intoKA sub-field for obtaining a time stepΔtThe following:
building points within a target region（x，y）Over time in the environmenttDiscrete time of partial differential equation set of change curve, based on finite difference method, for point in target region（x，y）Over time in the environmenttAnd carrying out numerical value dispersion on the partial differential equation set of the change curve to obtain a second dispersion equation set. Wherein the second set of discrete equations includes points within the target region（x，y）The simulation value of the ecological environment element istFirst order finite difference equation in direction, and, points within the target region（x，y）The simulation value of the ecological environment element istSecond order finite difference equations in direction.
Wherein the target area is internally dotted（x，y）The simulation value of the ecological environment element istThe first order finite difference equation in direction is as follows:
points within the target area（x，y）The simulation value of the ecological environment element istThe second order finite difference equation in direction is as follows:
and S103, determining a high-precision curved surface modeling finite difference equation set based on the first discrete equation set and the second discrete equation set.
The first discrete equation set and the second discrete equation set are combined to obtain a space-time collaborative High Accuracy Surface modeling method (HASM-ST for short) intAt the first momentnThe expression of finite difference of +1 iteration, namely the high-precision curved surface modeling finite difference equation system of the instant space synergy, is as follows:
wherein the high-precision curved surface of the spatio-temporal synergy models the initial conditions, i.e. positions, of the finite difference equation seti，j) Is located intInitial value of iteration of time
Comprises the following steps:
in the formula (I), the compound is shown in the specification,nrepresenting the iteration times, wherein n is a positive integer;trepresents time, and t is an integer of 0 or more;i、jrespectively is the row and column coordinates of grid points on the curved surface of the ecological environment element;xis the geographical abscissa of the point or points,yis the geographic ordinate of the point;Δxrepresenting ecological environment elements on the curved surfacexThe iteration step in the direction;Δyrepresenting ecological environment elements on the curved surfaceyThe iteration step in the direction;
to representtGrid point on curved surface of time ecological environment element（i，j）To be treated withnThe value of the secondary iteration;
、 
、
、
are respectively astGrid point on curved surface of time ecological environment element（i，j）To
To (1) anThe value of the secondary iteration;
a second class of Criserverer symbols which are ecological environment element curved surfaces;
is composed oftGrid point on curved surface of time ecological environment element（i，j）To the second basic quantityLTo (1) anThe value of the secondary iteration;
、
are respectively astGrid point on curved surface of time ecological environment element（i，j）To basic quantity of the first kindE、GTo (1) anThe value of the secondary iteration;Δtrepresents a time step;
indicating points（x，y）Over time in the environmenttCurve of changeA second class of cristokes symbols.
Is provided with
，
Is composed oftThe first of grid points on the curved surface of the time ecological environment elementnThe value of the sub-iteration is taken,
for the initial value of the iteration, the first equation in the equation set of equation (10) can be expressed as:
wherein A is a coefficient matrix of a first equation in the equation set of formula (10),
is the right-hand term of the first equation in the system of equations of equation (10),
by
And (4) calculating.
Similarly, the second equation in the equation set of equation (10) can be expressed as:
wherein B is a coefficient matrix of a second equation in the equation set of formula (10),
is the right-hand term of the second equation in the equation set of equation (10),
by
And (4) calculating.
The high-precision finite difference equation system for modeling a spatio-temporal synergy represented by equation (10) can be abbreviated as:
（13）
for space surface modeling, the area without sampling points needs to be predicted according to the existing sampling point observation data during solving.
That is, the iterative solution is performed by converting the high-precision curved surface modeling finite difference equation system with space-time coordination into a least square problem with constraint, and the expression of the least square problem with constraint is as follows:
in the formula (I), the compound is shown in the specification,nrepresenting the number of iterations;
representtThe first grid point of each grid point on the curved surface of the time ecological environment elementnThe value of the sub-iteration is taken,trepresents time;
is thattDiscrete points on curved surface of time ecological environment element（i，j）The first of the simulation values of the ecological environment elementsnThe value of the sub-iteration is,nis a positive integer and is a non-zero integer,tis an integer greater than 0;i、jrespectively the row coordinates and the column coordinates of discrete points on the curved surface of the ecological environment element;I、Jrows of discrete grid points on a surface of an element of an ecological environmentNumber and column number;AandBmodeling a coefficient item of a finite difference equation set for the high-precision curved surface of the time-space coordination;
and
modeling a right-end term of a finite difference equation set for the high-precision curved surface of the time-space coordination;Sa sampling matrix constructed according to sampling points;krepresenting a sample vector.
The formula (14) is a least square problem constrained by a sampling point information equation, and based on the formula (14), the overall simulation error can be kept to be minimum under the condition that the ecological environment element simulation value at the sampling point is close to the observation value of the sampling point, so that the sampling information is fully utilized, and the result obtained by iterative solution is ensured to approach to the optimal simulation effect.
In order to simplify the calculation, the Lagrange factor method is adopted to carry out approximate solution, and sufficiently large real numbers are subjected toλFor a fixed time window P, the high-precision curved surface modeling finite difference equation set for spatio-temporal synergy can be expressed approximately as the following linear least squares problem:
in the formula (I), the compound is shown in the specification,
，
is thattDiscrete points on curved surface of time ecological environment element（i，j）The first of the simulation values of the ecological environment elementsnA secondary iteration value;trepresents time;AandBmodeling coefficient terms of a finite difference equation set for the high-precision curved surface of the time-space coordination;
and
modeling a right-end term of a finite difference equation set for the high-precision curved surface of the time-space coordination;Sa sampling matrix constructed according to sampling points;krepresenting a sampling vector;λis a preset real number.
By solving the equation set of the formula (15), the ecological environment element curved surface can be simulated one by one according to the time step length. After the iteration initial value is input into the equation set of the formula (15), the calculation can be carried outt+PThe surface simulation value of the ecological environment element at the momentt+PThe curved surface analog value of the ecological environment element at the moment can be used ast+2PAnd (3) carrying out next simulation on the initial curved surface at the moment (namely the next time window) until the simulation of the ecological environment element curved surface in the whole time period to be simulated. Therefore, when the ecological environment element simulation is carried out, the spatial correlation of the elements and the time constraint information are considered, the simulation precision is improved, and a foundation is laid for the HASM-ST to be applied to space-time big data simulation.
Step S104, inputting observation data of the ecological environment elements to be simulated, which are acquired in advance, in the target area and the initial curved surfaces of the ecological environment elements to be simulated, which are acquired in advance, into a space-time cooperative high-precision curved surface modeling finite difference equation set for iterative solution to obtain an ecological environment element simulation result; the observation data is time sequence observation data in a time period to be simulated; the initial curved surface is an ecological environment element curved surface at the initial moment of the time period to be simulated.
After the space-time collaborative high-precision curved surface modeling finite difference equation set is obtained, when the ecological environment elements of the target area are simulated, the observation data of the ecological environment elements to be simulated need to be obtained first, generally, the observation data of the ecological environment elements to be simulated are time sequence observation values of each sampling point in the target area, which are also called ecological environment element observation time sequences, and the observation values can be obtained by sampling historical ecological environment element data or observation data obtained from ground observation stations.
The observation data is time sequence observation data in a time period to be simulated. For example, in the case where the ecological environment element is taken as the daily average air temperature, if the daily average air temperature of the target area time zone from 2018, 1/2018, 12/31/2018 is to be simulated, the observation data also needs to be the daily average air temperature observation data of the area from 2018, 1/2018, 12/31/2018.
The initial curved surface is an ecological environment element curved surface at the initial moment of a time period to be simulated, is used for providing a driving field for a space-time collaborative high-precision curved surface modeling finite difference equation set, can be generated by a computer software (such as ArcMap) in an arbitrary interpolation method or other models, and can also be obtained by simulating a traditional HASM. For example, when the daily average air temperature of the target area time zone from 2018, 1/2018 to 2018, 12/31/2018 needs to be simulated, the initial curved surface is daily average air temperature grid data corresponding to 2018, 1/2018.
When an initial curved surface is constructed through a traditional HASM, inputting observation data of the ecological environment elements to be simulated, which are acquired in advance, in a target area and the initial curved surface of the ecological environment elements to be simulated, which is acquired in advance, into a space-time cooperative high-precision curved surface modeling finite difference equation set for iterative solution to obtain an ecological environment element simulation result, wherein the method specifically comprises the following steps: inputting the initial curved surface of the ecological environment element to be simulated and observation data of the ecological environment element to be simulated corresponding to the initial time of the simulation time period into a traditional high-precision curved surface modeling equation set for curved surface simulation to obtain an iteration initial value; and inputting the iteration initial value into a space-time cooperative high-precision curved surface modeling finite difference equation set according to a preset time step for iterative solution to obtain a time sequence of the ecological environment element simulation result, namely a high-precision simulation result grid time sequence.
In the embodiment of the application, the initial curved surface of the ecological environment element to be simulated and the observation data of the ecological environment element to be simulated corresponding to the initial time of the simulation time period are input into the traditional high-precision curved surface modeling equation set for curved surface simulation, and an iteration initial value, namely the initial curved surface, is obtained. For example, if the daily average temperature of the target area time zone from 2018 year 1 month 1 day to 2018 year 12 month 31 day needs to be simulated, the initial time of the simulation time zone is 2018 year 1 month 1 day, and the simulation process may include the following steps:
step 1, inputting daily average air temperature grid data corresponding to 1/2018 as an initial curved surface and daily average air temperature observation data of 1/2018 to a traditional HASM (Hash-Sham) for simulation to obtain a simulation result of an initial time of a simulation time period, namely the simulation result of the initial time of the simulation time periodt 0 And (5) simulation results of the time.
Step 2, the time step length is advanced by one step, andt 1 simulating the curved surface of the ecological environment element at the moment, wherein the time step length of the scene of which the ecological environment element is daily average temperature is 1 day, at the moment,t 1 the time corresponds to 1 month and 2 days in 2018. To be provided witht 0 The simulation result of the time (1 month and 1 day in 2018) is used as an initial curved surfacet 1 Daily average air temperature observation data corresponding to the time (1 month and 2 days in 2018) is used as a constraint condition, HASM-ST is input to carry out daily average air temperature simulation, and the daily average air temperature is obtainedt 1 The daily average air temperature at that time is simulated.
Step 3, repeating the step 2 for iteration according to a time axis (1/2018-12/31/2018) by taking 1 day as a time step, and sequentially obtainingt 2 、t 3 、……t N The daily average air temperature at that time is simulated, wherein,t N indicating the end of the time period to be simulated, i.e. 12 months and 31 days in 2018.
According to the steps, a time sequence of the simulation results of the ecological environment elements in the time period to be simulated, namely a daily average air temperature simulation result grid time sequence of each day from 1 month and 1 day in 2018 to 12 months and 31 days in 2018 is obtained.
In summary, in the embodiment of the present application, the pairstPerforming finite difference dispersion on a partial differential equation set of the ecological environment element curved surface of the moment target area to obtain a first dispersion equation set; for points in the target area（x，y）Over time in the environmenttCarrying out finite difference dispersion on the partial differential equation set of the change curve to obtain a second dispersion equation set; based on a first discrete squareDetermining a high-precision curved surface modeling finite difference equation set of space-time coordination by the equation set and the second discrete equation set; and inputting the observation data of the ecological environment element to be simulated, which is acquired in advance, in the target area and the initial curved surface of the ecological environment element to be simulated, which is acquired in advance, into a space-time cooperative high-precision curved surface modeling finite difference equation set for iterative solution to obtain an ecological environment element simulation result. When the ecological environment element is simulated, the method provided by the steps not only considers the spatial correlation, but also sufficiently combines the inherent time dimension information, thereby improving the precision of the simulation result of the ecological environment element.
Exemplary applications
Taking a target area as a certain area of China as an example, the traditional HASM and the HASM-ST provided by the application are respectively applied to simulate the daily average temperature of the area in 2018, and the error evaluation is carried out on the simulation results of the traditional HASM and the HASM-ST by combining the temperature observation data of the ground meteorological site.
The indicators for error evaluation are Root Mean Square Error (RMSE) and correlation coefficient (R). Wherein, the calculation formula of the Root Mean Square Error (RMSE) is as follows:
the correlation coefficient (R) is calculated as follows:
in the formula (I), the compound is shown in the specification,Nrepresents the number of ground weather stations,p i denotes the number of HASM or HASM-ST derivediThe daily average air temperature simulation result at each ground meteorological station,o i denotes the firstiDaily average air temperature observed values of the ground meteorological stations;
the results of daily mean air temperature simulations for HASM or HASM-STA value;
represents the mean of the daily average air temperature observations for all ground meteorological sites.
Fig. 3 shows a Root Mean Square Error (RMSE) comparison (partially extracted from the daily average air temperature simulation results of 2018) between the daily average air temperature simulation results of the HASMs and the HASM-ST and the daily average air temperature observation data of the ground weather site, fig. 4 shows a correlation coefficient (R) comparison (partially extracted from the daily average air temperature simulation results of 2018) between the daily average air temperature simulation results of the HASMs and the HASM-ST and the daily average air temperature observation data of the ground weather site, table 1 shows a Root Mean Square Error (RMSE), a correlation coefficient (R) and a median between the daily average air temperature simulation results of the HASMs and the HASM-ST (all year 2018) and the daily average air temperature observation data of the ground weather site, table 1 is as follows:
as can be seen from fig. 3, 4 and table 1, compared with the conventional HASM, the simulation result of HASM-ST on daily average air temperature has lower root mean square error and higher correlation, and the above results show that the accuracy of the simulation result is improved by simulating the ecological environment elements based on the HASM-ST method compared with the conventional HASM.
Exemplary System
The embodiment of the present application provides a space-time collaborative high-precision curved surface modeling system, as shown in fig. 5, the system includes: a first discrete unit 501, a second discrete unit 502, a joint unit 503 and a solving unit 504. Wherein:
a first discrete unit 501 configured as a pairtAnd carrying out finite difference dispersion on the partial differential equation set of the ecological environment element curved surface of the moment target area to obtain a first discrete equation set.
A second discrete unit 502 configured to pair points within the target area（x，y）Over time in the environmenttPartial differential equation of change curveAnd carrying out finite difference discretization on the set to obtain a second discrete equation set.
A joint unit 503 configured to determine a high-precision curved surface modeling finite difference equation set of the spatio-temporal coordination based on the first discrete equation set and the second discrete equation set.
A solving unit 504 configured to input observation data of the pre-acquired ecological environment element to be simulated in the target area and the pre-acquired initial curved surface of the ecological environment element to be simulated into a spatio-temporal collaborative high-precision curved surface modeling finite difference equation set for iterative solution to obtain an ecological environment element simulation result; the observation data is time sequence observation data in a time period to be simulated; the initial curved surface is an ecological environment element curved surface at the initial moment of the time period to be simulated.
The space-time collaborative high-precision curved surface modeling system provided by the embodiment of the application can realize the steps and the flows of the space-time collaborative high-precision curved surface modeling method provided by any one of the above embodiments, and achieve the same technical effects, which are not described in detail herein.
The above description is only a preferred embodiment of the present application and is not intended to limit the present application, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present application shall be included in the protection scope of the present application.
Claims (9)
1. A high-precision curve modeling method based on space-time collaboration is characterized by comprising the following steps:
to pairtPerforming finite difference dispersion on a partial differential equation set of the ecological environment element curved surface of the moment target area to obtain a first dispersion equation set;
for points in the target area（x，y）Over time in the environmenttCarrying out finite difference dispersion on the partial differential equation set of the change curve to obtain a second discrete equation set;
determining a high-precision curved surface modeling finite difference equation set of space-time coordination based on the first discrete equation set and the second discrete equation set;
the high-precision curved surface modeling finite difference equation set of the time-space coordination is as follows:
the initial conditions of the space-time collaborative high-precision curved surface modeling finite difference equation set are as follows:
in the formula (I), the compound is shown in the specification,nrepresenting the number of iterations;trepresents time;i、jrespectively is the row and column coordinates of grid points on the curved surface of the ecological environment element;xis the geographical abscissa of the point or points,yis the geographic ordinate of the point;Δxrepresenting ecological environment elements on the curved surfacexThe iteration step in the direction;Δyrepresenting ecological environment elements on the curved surfaceyThe iteration step in the direction;
to representtGrid point on curved surface of time ecological environment element（i，j）To get it atnThe value of the secondary iteration;
are respectively astGrid point on curved surface of time ecological environment element（i，j）To
To (1) anThe value of the secondary iteration;
a second class of Criserverer symbols which are ecological environment element curved surfaces;
is composed oftGrid point on curved surface of time ecological environment element（i，j）To the second basic quantityLTo (1) anThe value of the secondary iteration;
、
are respectively astGrid point on curved surface of time ecological environment element（i，j）To basic quantity of the first kindE、GTo (1) anThe value of the secondary iteration;Δtrepresents a time step;
indicating points（x，y）Over time in the environmenttA second class of Criserverer symbols of the variation curve;
indicating points（x，y）Over time in the environmenttA second base quantity of the profile;
indicating points（x，y）Over time in the environmenttA first base quantity of the profile;
is composed oft-1Grid point on curved surface of time ecological environment element（i，j）To
、
A value of (d);
inputting observation data of the ecological environment elements to be simulated, which are acquired in advance, in the target area and the initial curved surfaces of the ecological environment elements to be simulated, which are acquired in advance, into the space-time cooperative high-precision curved surface modeling finite difference equation set for iterative solution to obtain an ecological environment element simulation result; the observation data is time sequence observation data in a time period to be simulated; the initial curved surface is an ecological environment element curved surface at the initial moment of the time period to be simulated.
2. The spatio-temporal collaborative high-precision curved surface modeling method according to claim 1, wherein the spatio-temporal collaborative high-precision curved surface modeling method is characterized in thattThe partial differential equation set of the ecological environment element curved surface of the time target area is as follows:
wherein:
，
in the formula (I), the compound is shown in the specification,fis the curved surface of the ecological environment element;f（x，y）is a point（x，y）Simulating the value of the ecological environment element;xis the geographical abscissa of the point or points,yis the geographic ordinate of the point;f x is composed offIn thatxA first partial derivative of the direction;f y is composed offIn thatyA first partial derivative of the direction;f xx is composed offIn thatxSecond partial derivatives of direction;f yy is composed offIn thatySecond partial derivatives of direction;E、F、Ga first type basic quantity of the curved surface of the ecological environment element;E x is composed ofEIn thatxA first partial derivative of the direction;E y is composed ofEIn thatyA first partial derivative of the direction;F x is composed ofFIn thatxA first partial derivative of the direction;F y is composed ofFIn thatyA first partial derivative of direction;G x is composed ofGIn thatxA first partial derivative of the direction;G y is composed ofGIn thatyA first partial derivative of direction;L、Nthe second kind of basic quantity is the curved surface of the ecological environment element;
the second class of Criserverer symbols is the curved surface of the ecological environment element.
3. The spatio-temporal collaborative high-precision curved surface modeling method according to claim 1, wherein the first set of discrete equations includestTime point（x，y）The simulation values of the elements in the ecological environment are respectivelyx、yA first order finite difference equation in direction, and,ttime point（x，y）The simulation value of the ecological environment element isx、yA second order finite difference equation in direction.
4. The spatio-temporal collaborative high-precision curved surface modeling method according to claim 1, wherein the points in the target region（x，y）Over time in the environmenttThe partial differential equation of the change curve is:
wherein the content of the first and second substances,
，
in the formula (I), the compound is shown in the specification,vindicating points（x，y）Over time in the environmenttA change curve;v t to representvIn thattA first partial derivative of the direction;v tt to representvIn thattSecond partial derivatives of direction;
indicating points（x，y）Over time in the environmenttA first base quantity of the profile;
indicating points（x，y）Over time in the environmenttA second base quantity of the profile;
indicating points（x，y）Over time in the environmenttA second class of Criserverer symbols of the variation curve;
is composed of
To timetThe derivative of (a) of (b),
。
5. the spatio-temporal collaborative high-precision surface modeling method according to claim 1, wherein the second set of discrete equations includes points within a target region（x，y）The simulation value of the ecological environment element istFirst order finite difference equation in direction, and, points within the target region（x，y）The simulation value of the ecological environment element istSecond order finite difference equations in direction.
6. The spatio-temporal collaborative high-precision curved surface modeling method according to claim 1, wherein observation data of an ecological environment element to be simulated, which is acquired in advance in a target area, and an initial curved surface of the ecological environment element to be simulated, which is acquired in advance, are input to the spatio-temporal collaborative high-precision curved surface modeling finite difference equation set for iterative solution, so as to obtain an ecological environment element simulation result, specifically:
inputting the initial curved surface of the ecological environment element to be simulated and observation data of the ecological environment element to be simulated corresponding to the initial time of the simulation time period into a traditional high-precision curved surface modeling equation set for curved surface simulation to obtain an iteration initial value;
and inputting the iteration initial value to the space-time cooperative high-precision curved surface modeling finite difference equation set according to a preset time step for iterative solution to obtain a time sequence of ecological environment element simulation results.
7. The spatio-temporal collaborative high precision curved surface modeling method according to claim 1, characterized in that the iterative solution is performed by converting the spatio-temporal collaborative high precision curved surface modeling finite difference equation set into a constrained least squares problem, the constrained least squares problem expression is as follows:
in the formula (I), the compound is shown in the specification,nrepresenting the number of iterations;
to representtThe first grid point of each grid point on the curved surface of the time ecological environment elementnThe value of the secondary iteration;
，trepresents time;
is thattDiscrete points on curved surface of time ecological environment element（i，j）The first of the simulation values of the ecological environment elementsnThe value of the sub-iteration is,nis a positive integer and is a non-zero integer,tis an integer greater than 0;i、jrespectively is the row and column coordinates of grid points on the curved surface of the ecological environment element;I、Jthe number of rows and columns of discrete grid points on the curved surface of the ecological environment element;AandBmodeling coefficient terms of a finite difference equation set for the high-precision curved surface of the time-space coordination;
and
modeling a right-end term of a finite difference equation set for the high-precision curved surface of the time-space coordination;Sa sampling matrix constructed according to sampling points;krepresenting a sample vector.
8. The spatio-temporal collaborative high precision curved surface modeling method according to claim 7, characterized in that the lagrangian factor method is adopted to convert the spatio-temporal collaborative high precision curved surface modeling finite difference equation set into a linear least squares problem, and the expression of the linear least squares problem is as follows:
in the formula (I), the compound is shown in the specification,
，
is thattDiscrete points on curved surface of time ecological environment element（i，j）The first of the simulation values of the ecological environment elementsnA secondary iteration value;trepresents time;AandBmodeling coefficient terms of a finite difference equation set for the high-precision curved surface of the time-space coordination;
and
modeling a right-end term of a finite difference equation set for the high-precision curved surface of the time-space coordination;Sa sampling matrix constructed according to sampling points;krepresenting a sampling vector;λis a preset real number.
9. A spatiotemporal collaborative high-precision curved surface modeling system, comprising:
a first discrete unit configured as a pairtPerforming finite difference dispersion on a partial differential equation set of the ecological environment element curved surface of the moment target area to obtain a first dispersion equation set;
a second discrete unit configured to pair points in the target region（x，y）Over time in the environmenttCarrying out finite difference dispersion on the partial differential equation set of the change curve to obtain a second dispersion equation set;
the joint unit is configured to determine a high-precision curved surface modeling finite difference equation set based on the first discrete equation set and the second discrete equation set;
the high-precision curved surface modeling finite difference equation set of the time-space coordination is as follows:
the initial conditions of the space-time collaborative high-precision curved surface modeling finite difference equation set are as follows:
in the formula (I), the compound is shown in the specification,nrepresenting the number of iterations;trepresents time;i、jrespectively is the row and column coordinates of grid points on the curved surface of the ecological environment element;xis the geographical abscissa of the point or points,yis the geographic ordinate of the point;Δxrepresenting ecological environment elements inxThe iteration step in the direction;Δyrepresenting ecological environment elements on the curved surfaceyThe iteration step in the direction;
to representtGrid point on curved surface of time ecological environment element（i，j）To get it atnThe value of the secondary iteration;
are respectively astGrid point on curved surface of time ecological environment element（i，j）To
To (1) anThe value of the secondary iteration;
a second class of Criserverer symbols which are ecological environment element curved surfaces;
is composed oftGrid point on curved surface of time ecological environment element（i，j）To the second basic quantityLTo (1) anThe value of the secondary iteration;
、
are respectively astGrid point on curved surface of time ecological environment element（i，j）To basic quantity of the first kindE、GTo (1) anThe value of the secondary iteration;Δtrepresents a time step;
indicating points（x，y）By treating the elements of the ecological environment over timetA second class of Criserverer symbols of the variation curve;
indicating points（x，y）Over time in the environmenttA second base quantity of the profile;
indicating points（x，y）Over time in the environmenttA first base quantity of the profile;
is composed oft-1Grid point on curved surface of time ecological environment element（i，j）To
、
A value of (d);
the solving unit is configured to input observation data of the ecological environment elements to be simulated, which are acquired in advance, in the target area and initial curved surfaces of the ecological environment elements to be simulated, which are acquired in advance, into the space-time cooperative high-precision curved surface modeling finite difference equation set for iterative solution to obtain an ecological environment element simulation result; the observation data is time sequence observation data in a time period to be simulated; the initial curved surface is an ecological environment element curved surface at the initial moment of the time period to be simulated.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202211306422.2A CN115374682B (en) | 2022-10-25 | 2022-10-25 | Space-time collaborative high-precision curved surface modeling method and system |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202211306422.2A CN115374682B (en) | 2022-10-25 | 2022-10-25 | Space-time collaborative high-precision curved surface modeling method and system |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN115374682A CN115374682A (en) | 2022-11-22 |
| CN115374682B true CN115374682B (en) | 2023-01-03 |
Family
ID=84073972
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202211306422.2A Active CN115374682B (en) | 2022-10-25 | 2022-10-25 | Space-time collaborative high-precision curved surface modeling method and system |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN115374682B (en) |
Families Citing this family (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115795402B (en) * | 2023-02-10 | 2023-04-07 | 中国科学院地理科学与资源研究所 | Variational method-based multi-source precipitation data fusion method and system |
| CN116090315B (en) * | 2023-04-07 | 2023-06-13 | 中国科学院地理科学与资源研究所 | Precipitation space distribution simulation method considering space heterogeneity and data real-time update |
| CN116108761B (en) * | 2023-04-12 | 2023-06-27 | 中国科学院地理科学与资源研究所 | Regional climate simulation method and system for coupling deep learning and HASM |
| CN117275756A (en) * | 2023-08-25 | 2023-12-22 | 中国科学院地理科学与资源研究所 | Infectious disease space-time diffusion simulation method and system based on HASM |
| CN117875091B (en) * | 2024-03-12 | 2024-05-10 | 中国科学院地理科学与资源研究所 | Optimization method and device of high-precision curved surface modeling method based on adaptive algorithm |
Family Cites Families (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103077274B (en) * | 2013-01-05 | 2015-09-23 | 中国科学院地理科学与资源研究所 | High Accuracy Surface Modeling Intelligentized method and device |
| CN106683185B (en) * | 2017-01-09 | 2020-04-03 | 中国科学院地理科学与资源研究所 | High-precision curved surface modeling method based on big data |
| CN106934860B (en) * | 2017-01-12 | 2019-12-31 | 天津大学 | Three-dimensional geological modeling method based on T-spline |
| US10593024B2 (en) * | 2018-04-04 | 2020-03-17 | Hong Kong Applied Science And Technology Research Institute Co., Ltd. | Image inpainting on arbitrary surfaces |
-
2022
- 2022-10-25 CN CN202211306422.2A patent/CN115374682B/en active Active
Also Published As
| Publication number | Publication date |
|---|---|
| CN115374682A (en) | 2022-11-22 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN115374682B (en) | Space-time collaborative high-precision curved surface modeling method and system | |
| Landis et al. | Bayesian analysis of biogeography when the number of areas is large | |
| Yue et al. | High-accuracy surface modelling and its application to DEM generation | |
| Wang et al. | Land use optimization modelling with ecological priority perspective for large-scale spatial planning | |
| Long et al. | Reconstruction of historical arable land use patterns using constrained cellular automata: A case study of Jiangsu, China | |
| Li et al. | Efficient dimension reduction and surrogate-based sensitivity analysis for expensive models with high-dimensional outputs | |
| Hugosson | Quantifying uncertainties in a national forecasting model | |
| Liu et al. | Simulating the conversion of rural settlements to town land based on multi-agent systems and cellular automata | |
| CN108376183A (en) | A kind of city CA model construction method based on principle of maximum entropy | |
| Gholami et al. | Narrowing uncertainties in forecasting urban building energy demand through an optimal archetyping method | |
| CN103544385A (en) | Multi-scale spatial load predicting method balancing spatial heterogeneity | |
| Melo et al. | Determining spatial resolution in spatial load forecasting using a grid-based model | |
| Ozah et al. | A deterministic cellular automata model for simulating rural land use dynamics: A case study of Lake Chad Basin | |
| Voudouri et al. | Objective calibration of numerical weather prediction models | |
| Li et al. | Uncertainty modelling and analysis of volume calculations based on a regular grid digital elevation model (DEM) | |
| Budamala et al. | Enhance the prediction of complex hydrological models by pseudo-simulators | |
| CN109033181B (en) | Wind field geographic numerical simulation method for complex terrain area | |
| Popinet et al. | A quadtree-adaptive spectral wave model | |
| Collins et al. | A posteriori error estimation for the Lax–Wendroff finite difference scheme | |
| Zhao et al. | LandSys II: Agent-based land use–forecast model with artificial neural networks and multiagent model | |
| Zhao et al. | Sensitivity studies of a high accuracy surface modeling method | |
| Zhang et al. | Self-modifying CA model using dual ensemble Kalman filter for simulating urban land-use changes | |
| CN102880753B (en) | Based on the land utilization space characteristic dimension conversion method of fractal dimension | |
| Zhao et al. | Examining Land-Use Change Trends in Yucheng District, Ya’an City, China, Using ANN-CA Modeling | |
| Kim et al. | Spatial diffusion modeling of new residential area for land-use planning of rural villages |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |