CN107590346B - Downscaling correction model based on spatial multi-correlation solution set algorithm - Google Patents
Downscaling correction model based on spatial multi-correlation solution set algorithm Download PDFInfo
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Abstract
The invention discloses a downscaling correction method based on a spatial multiple correlation solution set algorithmA model comprising the steps of: step (1) data acquisition, including climate mode grid data series Xt＝(x1,t,x2,t,…,xm,t) Where m is the number of grids, t represents the time, and the measured data series Y of each sitet＝(y1,t,y2,t,…,yn,t) Wherein n is the number of sites; step (2) establishing a down-scale correction model based on a space multiple correlation solution set algorithm: y ═ B + AX + epsilon (epsilon. N (0, sigma.))2) A and B) are used for reflecting the relevant structural relationship between the grid data and the site measured data, and epsilon is a standardized independent random vector; and (3) solving the coefficient matrixes A and B in the formula (1) by adopting a particle swarm optimization algorithm, and the method has the characteristic of improving the simulation precision.
Description
Technical Field
The invention relates to a downscaling correction model based on a spatial multiple correlation solution set algorithm, and belongs to the technical field of statistical downscaling.
Background
According to specific information of global climate patterns, the spatial resolution of the patterns is low, and most of the patterns are 1.5 ° × 1.5 ° or more. If the mode data are directly used for researching the influence of climate change on hydrological water resources, great errors are certainly brought, the result has high uncertainty, and the scale reduction processing is carried out on the climate mode for researching the future climate change of the region.
Common downscaling methods include dynamic downscaling, statistical downscaling, and interpolation downscaling. The statistical downscaling method is simple and flexible, is easy to implement, and is widely applied in practice. Currently, a common statistical downscaling method (such as SDSM, ASD, etc.) is to construct a statistical relationship between a forecast variable and a forecast factor to calculate a downscaling result of the forecast variable of each station in an area. However, there may not be a clear physical correlation between the predictor(s) and the predictor variables; when the correlation between the forecasting factor and the forecasting variable is weak, the error of the downscaling result is larger, and higher uncertainty exists; such a downscaling method by introducing various predictor factors may "pollute" the downscaling result of the predictor variable. In addition, the common statistical downscaling method can only realize downscaling of a single site generally, and cannot guarantee spatial correlation of downscaling results of all sites in an area.
Disclosure of Invention
The invention aims to solve the technical problem of providing a reduced scale correction model based on a space multiple correlation solution set algorithm, which can improve the simulation precision
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
the down-scale correction model based on the space multiple correlation solution set algorithm comprises the following steps:
step (1) data acquisition, including climate mode grid data series Xt＝(x1,t,x2,t,…,xm,t) Where m is the number of grids, t represents the time, and the measured data series Y of each sitet＝(y1,t,y2,t,…,yn,t) Wherein n is the number of sites;
step (2) establishing a down-scale correction model based on a space multiple correlation solution set algorithm, wherein the down-scale correction model is as the following formula (1):
Y＝B+AX+ε(ε～N(0,σ2)) (1)
wherein A and B are used for reflecting the correlation structure relationship between the grid data and the site measured data, epsilon is a standardized independent random vector, and the formula (1) is developed into a matrix form:
and (3) solving the coefficient matrixes A and B in the formula (1) by adopting a particle swarm optimization algorithm.
In the step (2), according to the rule that the greater the correlation coefficient is, the better the correlation coefficient is, for each stationThe grid points with high correlation are screened out, and a site y is setiThe corresponding set of p grid points with the highest correlation is C ═ xj1,xj2,...,xjp) The constraint conditions are set for the coefficient matrix a as shown in the following equation (3):
where i denotes the ith station and j denotes the jth grid point.
In the particle swarm optimization algorithm in the step (3), a group of parameters A and B are regarded as one particle, each particle in the swarm represents one candidate solution in the model optimization problem, and the ith particle PiCan be represented as Pi＝(Ai,Bi),i＝1,2,…,m。
The method specifically comprises the following steps:
initializing a particle group, determining the number of the particle group, the speed and the position of each particle, setting a particle group consisting of m particles in a d-dimensional target search space, XkRepresenting the position of each particle in the population at the kth iteration, i.e.
Wherein
Represents a particle PiIn a position of
The velocity of each particle in the corresponding population is denoted VkI.e. by
Wherein Vi kRepresents a particle PiOf speed, i.e.
Evaluating the fitness of each particle;
comparing the current adaptive value of each particle with the historical individual optimal adaptive value, if the current adaptive value is superior to the historical optimal adaptive value, taking the current adaptive value as a new historical optimal adaptive value, and recording the optimal position of each particle, wherein the position of the individual optimal particle is expressed as
Wherein
Is a particle PiAt an optimum position, i.e.
Then comparing the historical optimal adaptation value and the global optimal adaptation value of each particle, if the historical optimal adaptation value of a certain particle is superior to the global optimal adaptation value, the historical optimal adaptation value of the particle is used as a new global optimal adaptation value, and simultaneously, the position of the global optimal particle is recorded,
representing a global optimal particle position;
in the iterative process of the particles, the positions and the speeds of the particles are updated through the individual optimal particle positions and the global optimal particle positions, and in k +1 iterations, the speeds and the positions of the particle groups are updated according to the formula (4) and the formula (5):
Xk+1＝Xk+Vk+1(5)
where ω is the inertial weight, c1And c2Is a constant, called the learning factor, r1And r2Is distributed in [0,1 ]]A random number of intervals;
and judging whether the global optimal adaptive value reaches the optimal value, continuing iteration when the global optimal adaptive value does not reach the optimal value, and determining a downscaling correction model according to the corresponding optimal particles, namely the downscaling model coefficient matrixes A and B when the global optimal adaptive value reaches the optimal value.
And evaluating the quality performance of each particle in the population by adopting a fitness function, wherein the fitness function is as follows:
in order to prevent the particles from moving away from the search space during the updating process to cause search missing in a small range, the maximum search range X is setmaxTo control the maximum speed at which the particles fly.
The invention achieves the following beneficial effects: the downscaling correction model based on the spatial multiple correlation solution set algorithm directly solves the climate mode data, considers the correlation of precipitation/air temperature in space to a certain degree, realizes the downscaling processing of the climate mode, ensures that the precipitation/air temperature after downscaling can keep the inherent space dependent structure, realizes the correction function of the climate mode, and can obviously improve the simulation precision.
Drawings
FIG. 1 is a schematic flow chart of a down-scale correction model based on a spatial multi-correlation solution set algorithm according to the present invention;
FIG. 2 is a comparison graph of a simulation process and an actual measurement process of the monthly rainfall amount of the scale reduction after the scale reduction of the climate mode of the yellow river source area from 1961 to 2004.
Detailed Description
The invention is further described below with reference to the accompanying drawings. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
As shown in figure 1 of the drawings, in which,
step 1: data acquisition, including 1) acquiring day-by-day rainfall grid data X from IPCC official website in 1961 to 2004 in different climate modes of yellow river source areat＝(x1,t,x2,t,…,xm,t) M is the number of grids, t represents the time; 2) collecting measured rainfall data Y day by day from 1961 to 2004 of each site in yellow river source areat＝(y1,t,y2,t,…,yn,t) And n is the number of stations. The benchmark period (1961-.
Step 2: and establishing a down-scale correction model based on a space multiple correlation solution set algorithm. The down-scale correction model based on the space multiple correlation solution set comprises the following steps:
Y＝B+AX+ε(ε～N(0,σ2)) (1)
wherein A and B reflect the correlation structure relationship between the grid data and the site measured data, epsilon is a standardized independent random vector, and the above formula is developed by a matrix form as follows:
in practice, it is unlikely that a site will correlate as highly with each grid point of the climate pattern. Therefore, according to the rule that the larger the correlation coefficient is, the better the correlation coefficient is, the grid points with high correlation (the first four grid points are taken at this time) are screened out for each site. Set station yiThe corresponding best set of 4 grid points is C ═ xj1,xj2,xj3,xj4) So there should be a constraint for the coefficient matrix a:
where i is the ith station and j is the jth grid point.
And step 3: solving coefficient matrixes A and B in the formula (1) by adopting a particle swarm optimization algorithm, regarding a group of parameters A and B as a particle, enabling each particle in the population to represent a candidate solution in the model optimization problem, and enabling the ith particle PiCan be represented as Pi＝(Ai,Bi),i＝1,2,…,m；
Initializing a particle group, determining the number of the particle group, the speed and the position of each particle, setting the particle group consisting of m particles in a d-dimensional target search spaceBody, XkRepresenting the position of each particle in the population at the kth iteration, i.e.
Wherein
Represents a particle PiIn a position of
The velocity of each particle in the corresponding population is denoted VkI.e. by
Wherein Vi kRepresents a particle PiOf speed, i.e.
Evaluating the fitness of each particle, and evaluating the performance of each particle in the population by adopting a fitness function, wherein the fitness function is as follows:
comparing the current adaptive value of each particle with the historical individual optimal adaptive value, if the current adaptive value is superior to the historical optimal adaptive value, taking the current adaptive value as a new historical optimal adaptive value, and recording the optimal position of each particle, wherein the position of the individual optimal particle is expressed as
Wherein
Is a particle PiAt an optimum position, i.e.
Then comparing the historical best fit of each particleA response value and a global optimal adaptation value, if the historical optimal adaptation value of a certain particle is superior to the global optimal adaptation value, the historical optimal adaptation value of the particle is used as a new global optimal adaptation value, and the position of the global optimal particle is recorded at the same time,
representing a global optimal particle position;
in the iterative process of the particles, the positions and the speeds of the particles are updated through the individual optimal particle positions and the global optimal particle positions, and in k +1 iterations, the speeds and the positions of the particle groups are updated according to the formula (4) and the formula (5):
Xk+1＝Xk+Vk+1(5)
where ω is the inertial weight, c1And c2Is a constant, called the learning factor, r1And r2Is distributed in [0,1 ]]A random number of intervals;
and judging whether the global optimal adaptive value reaches the optimal value, continuing iteration when the global optimal adaptive value does not reach the optimal value, and determining a downscaling correction model according to the corresponding optimal particles, namely the downscaling model coefficient matrixes A and B when the global optimal adaptive value reaches the optimal value.
In order to prevent the particles from moving away from the search space during the updating process to cause search missing in a small range, the maximum search range X is setmaxTo control the maximum speed at which the particles fly.
The model simulation process and the actual measurement process of the rainfall by month in the comparison ratio regular period and the verification period as shown in fig. 2 can find that the model simulation precision is greatly improved, and the simulation difference among the modes is small.
In the embodiment, three indexes are adopted to evaluate the simulation performance of the climate mode, namely a root mean square error RMSE, a correlation coefficient R and a certainty coefficient NSE. Suppose the measured series is Xobs,i(i ═ 1,2, …, n); the corresponding analog series is Xsim,i(i is 1,2, …, n) and n isThe total number of the series periods, each index, is calculated as follows. The evaluation index values of the monthly rainfall simulation performance in the rate period and the verification period after the 15 modes are downscaled are shown in the table 1.
(1) The root mean square error is the square root of the square of the average deviation between the analog value and the measured value, and reflects the accuracy of the analog value, and the smaller the value, the closer the analog value and the measured value are, the formula is:
(2) the correlation coefficient is used for describing the linear correlation degree between the simulation series and the actual measurement series, the closer the value is to 1, the higher the correlation degree is, the more uniformly distributed the correlation coefficient is on the 45-degree line of the X-Y correlation diagram, and the calculation formula is as follows:
in the above formula
And
the average values of the actual measurement series and the simulation series are respectively as follows.
(3) The certainty coefficient is a coefficient which represents the degree of coincidence between the simulation series and the actual measurement series and is also called as Nash efficiency coefficient, the closer the value is to 1, the higher the simulation precision of the mode is, and the calculation formula is as follows:
TABLE 1 weather mode post-treatment standard period monthly rainfall simulation Performance
The average measured month rainfall for years in the yellow river source area period (1961-; the RMSE index can also reflect the improvement of the mode simulation precision, the RMSE average value of the rate period is 18.73mm, and the RMSE average value of the verification period is 17.10 mm; the correlation between the analog value of each mode and the actual measurement is still good, and the correlation coefficient is above 0.87 no matter in the calibration period or the verification period; from the deterministic coefficient index, the process simulation of the monthly rainfall after the mode downscaling is more consistent with the actual measurement series, and the deterministic coefficients are all above 0.7. In conclusion, after the mode is subjected to downscaling treatment, the model rainfall simulation precision is high, and the statistical downscaling model provided by the invention is reasonable.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.
Claims (4)
1. The downscaling correction model based on the space multiple correlation solution set algorithm is characterized by comprising the following steps of:
step (1) data acquisition, including climate mode grid data series Xt＝(x1,t,x2,t,…,xm,t) Where m is the number of grids, t represents the time, and the measured data series Y of each sitet＝(y1,t,y2,t,…,yn,t) Wherein n is the number of sites;
step (2) establishing a down-scale correction model based on a space multiple correlation solution set algorithm, wherein the down-scale correction model is as the following formula (1):
Y＝B+AX+ε (1)，
wherein A and B are used to reflectThe related structure relationship between the grid data and the site measured data, wherein epsilon is a standardized independent random vector from epsilon to N (0, sigma)2) The formula (1) is developed in a matrix form as follows:
solving coefficient matrixes A and B in the formula (1) by adopting a particle swarm optimization algorithm;
the particle swarm optimization algorithm regards a group of parameters A and B as a particle, each particle in the population represents a candidate solution in the model optimization problem, and the ith particle PiCan be represented as Pi＝(Ai,Bi),i＝1,2,…,m；
The method specifically comprises the following steps:
initializing a particle group, determining the number of the particle group, the speed and the position of each particle, setting a particle group consisting of m particles in a d-dimensional target search space, XkRepresenting the position of each particle in the population at the kth iteration, i.e.
Wherein
Represents a particle PiIn a position of
The velocity of each particle in the corresponding population is denoted VkI.e. by
Wherein Vi kRepresents a particle PiOf speed, i.e.
Evaluating the fitness of each particle;
comparing the current adaptive value of each particle with the historical individual optimal adaptive value, if the current adaptive value is superior to the historical optimal adaptive value, taking the current adaptive value as a new historical optimal adaptive value, and recording the optimal position of each particle, wherein the position of the individual optimal particle is expressed as
Wherein
Is a particle PiAt an optimum position, i.e.
Then comparing the historical optimal adaptation value and the global optimal adaptation value of each particle, if the historical optimal adaptation value of a certain particle is superior to the global optimal adaptation value, the historical optimal adaptation value of the particle is used as a new global optimal adaptation value, and simultaneously, the position of the global optimal particle is recorded,
representing a global optimal particle position;
in the iterative process of the particles, the positions and the speeds of the particles are updated through the individual optimal particle positions and the global optimal particle positions, and in k +1 iterations, the speeds and the positions of the particle groups are updated according to the formula (4) and the formula (5):
Xk+1＝Xk+Vk+1(5)
where ω is the inertial weight, c1And c2Is a constant, called the learning factor, r1And r2Is distributed in [0,1 ]]A random number of intervals;
and judging whether the global optimal adaptive value reaches the optimal value, continuing iteration when the global optimal adaptive value does not reach the optimal value, and determining a downscaling correction model according to the corresponding optimal particles, namely the downscaling model coefficient matrixes A and B when the global optimal adaptive value reaches the optimal value.
2. The downscaling correction model based on the spatial multi-correlation solution set algorithm as claimed in claim 1, wherein in the step (2), the grid points with high correlation are selected for each site according to the rule that the larger the correlation coefficient is, the better the correlation coefficient is, and the site y is setiThe corresponding set of p grid points with the highest correlation is C ═ xj1,xj2,...,xjp) The constraint conditions are set for the coefficient matrix a as shown in the following equation (3):
where i denotes the ith station and j denotes the jth grid point.
3. The downscaling correction model based on the spatial multi-correlation solution set algorithm of claim 1, wherein a fitness function is used to evaluate the performance of each particle in the population, and the fitness function is:
4. the downscaling correction model for spatial multiplexing solution set algorithm according to claim 1, wherein to prevent the particles from moving away from the search space during the update process to cause the search missing in a small range, the maximum search range X is setmaxTo control the maximum speed at which the particles fly.
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