CN113917568A - Rainfall forecast capacity and remote correlation effect correlation method based on certainty coefficient - Google Patents

Rainfall forecast capacity and remote correlation effect correlation method based on certainty coefficient Download PDF

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CN113917568A
CN113917568A CN202111194642.6A CN202111194642A CN113917568A CN 113917568 A CN113917568 A CN 113917568A CN 202111194642 A CN202111194642 A CN 202111194642A CN 113917568 A CN113917568 A CN 113917568A
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CN113917568B (en
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赵铜铁钢
陈浩玲
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Sun Yat Sen University
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Abstract

The invention relates to the technical field of precipitation forecast, and provides a method for correlating precipitation forecast capacity and remote correlation action based on a certainty coefficient, which comprises the following steps: acquiring historical forecast precipitation data, observation precipitation data and a meteorological index sample sequence to obtain original sample data; establishing regression equations of the observed rainfall, the forecast rainfall, the meteorological indexes and a union set of the forecast rainfall and the meteorological indexes, and obtaining corresponding certainty coefficients through the regression equations respectively; respectively calculating the variance explained by the individually forecasted precipitation, the variance explained by the individually forecasted weather indicator and the variance repeatedly explained by the individually forecasted precipitation and the weather indicator based on set operation; processing the variance by using a bootstrap method to obtain reference distribution of the variance; and comparing the original sample data with the reference distribution of the variance to obtain a correlation result of the precipitation forecast capacity and the remote correlation effect, and effectively distinguishing the components of overlapping and difference in the precipitation forecast and the observed precipitation information provided by the meteorological factors.

Description

Rainfall forecast capacity and remote correlation effect correlation method based on certainty coefficient
Technical Field
The invention relates to the technical field of precipitation forecast, in particular to a method for associating precipitation forecast capacity and remote correlation action based on a certainty coefficient.
Background
The accurate seasonal rainfall forecast has important value and wide application prospect in the fields of disaster prevention and reduction, water resource planning and management and the like of natural disasters such as flooding, drought and the like. Hercino-southern billows (El)
Figure BDA0003302548540000011
Oscillotion, ENSO) phenomenon is an important driving factor for global seasonal precipitation abnormalities. Some studies will characterize meteorological factors of ENSO events (e.g.
Figure BDA0003302548540000012
And
Figure BDA0003302548540000013
etc.) as a forecasting factor, and forecasting seasonal precipitation by utilizing the remote correlation effect of meteorological factors on precipitation. On the other hand, meteorological and Climate centers in many countries and regions of the world begin to develop respective Global Climate Models (GCMs) which characterize various key physical processes related to Climate, and the forecast results have clear physical meanings.
Although weather factors and GCM precipitation forecast can provide information for seasonal precipitation, in practical application of the information, it is difficult to judge whether the GCM seasonal precipitation with certain physical meanings includes information of key remote correlation; in different regions of the world, the information provided by the meteorological factor and the GCM seasonal precipitation is redundant to a certain extent, and the information provided by the meteorological factor and the GCM seasonal precipitation is redundant to a certain extent. In order to solve these problems, it is necessary to provide a simple and practical method for determining the overlap and difference between the two information, so as to provide a certain reference for using the forecast information in the actual service.
Disclosure of Invention
The invention provides a rainfall forecast capacity and remote correlation function association method based on a certainty coefficient, and aims to solve the problems of overlapping and difference of rainfall forecast and key remote correlation function information in a global climate model season.
In order to solve the technical problems, the technical scheme of the invention is as follows:
a rainfall forecast capacity and remote correlation action correlation method based on certainty coefficients comprises the following steps:
s1, acquiring historical forecast precipitation data, observation precipitation data and meteorological index sample sequences to obtain original sample data;
s2, establishing regression equations of the observed precipitation, the forecast precipitation, the meteorological indexes and the union of the forecast precipitation and the meteorological indexes, and obtaining corresponding certainty coefficients through the regression equations respectively;
s3, respectively calculating the variance explained by the individually forecasted precipitation, the variance explained by the individually forecasted meteorological index and the variance repeatedly explained by the individually forecasted precipitation and the meteorological index based on set operation according to the certainty coefficient;
s4, processing the variances by using a bootstrap method to obtain reference distribution of the three variances;
and S5, comparing the original sample data with the reference distribution of the three variances to obtain a correlation result of the precipitation forecast capacity and the remote correlation action.
Compared with the prior art, the technical scheme of the invention has the beneficial effects that: the invention combines the collective operation and the linear regression certainty coefficient, and simply and effectively distinguishes the overlapping and different components in the observed rainfall information provided by the rainfall forecast and the meteorological factor, thereby providing reference for the business use of the rainfall forecast.
Drawings
Fig. 1 is a flowchart of a method for associating precipitation forecast capacity with a remote correlation in embodiment 1.
FIG. 2 is DJF
Figure BDA0003302548540000021
And the distribution diagram of the indexes and the observed precipitation correlation coefficient.
Fig. 3 is a spatial distribution diagram of deterministic coefficients.
FIG. 4 shows the forecast precipitation,
Figure BDA0003302548540000022
Providing a spatial distribution map of the independent and overlapping components of the information.
FIG. 5 is a diagram of forecast precipitation sums on a global grid
Figure BDA0003302548540000023
Information incidence relation classification situation distribution diagram。
FIG. 6 shows the sum of forecasted precipitation for eight different associations
Figure BDA0003302548540000024
Information wien diagram.
Detailed Description
The drawings are for illustrative purposes only and are not to be construed as limiting the patent;
it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
The technical solution of the present invention is further described below with reference to the accompanying drawings and examples.
Example 1
The present embodiment provides a method for associating a rainfall forecast capacity and a remote correlation based on a deterministic coefficient, as shown in fig. 1, which is a flowchart of the method for associating a rainfall forecast capacity and a remote correlation based on a deterministic coefficient.
The method for associating rainfall forecast capacity and remote correlation based on the certainty coefficient comprises the following steps:
and S1, acquiring historical forecast precipitation data, observation precipitation data and meteorological index sample sequences to obtain original sample data.
Wherein, the meteorological indexes contained in the obtained meteorological index sample sequence comprise
Figure BDA0003302548540000031
And/or
Figure BDA0003302548540000032
In this embodiment, the selection is made
Figure BDA0003302548540000033
As a meteorological index.
S2, establishing regression equations of the observed precipitation, the forecast precipitation, the meteorological indexes and the union of the forecast precipitation and the meteorological indexes, and obtaining corresponding certainty coefficients through the regression equations respectively.
In this step, the observation precipitation o is established respectivelykAnd forecast precipitation fkRegression equation of, observing precipitation okAnd weather indexes
Figure BDA0003302548540000034
And observing the precipitation okAnd forecasting the union of precipitation and meteorological indexes
Figure BDA0003302548540000035
Further, the certainty coefficient determined by the above three regression equations is obtained.
Wherein the precipitation o is observedkAnd forecast precipitation fkIs determined by the regression equation of2The calculation formula of (o to f) is as follows:
Figure BDA0003302548540000036
Figure BDA0003302548540000037
in the formula okRepresents observed precipitation data of the k year, fkThe forecast rainfall data of the kth year is represented, and K is the total year number of the rainfall data; alpha is alpha1And beta1Is an intercept term and a slope term of the linear regression model; epsilon1,kResidual terms of the linear regression model;
Figure BDA00033025485400000316
indicating the average observed precipitation over many years. Wherein the corresponding certainty factor can be obtained by comparing the sum of the squares of the residuals and observing the total variance of the precipitation.
By observing the precipitation okAnd weather indexes
Figure BDA00033025485400000315
Is determined by the regression equation
Figure BDA0003302548540000038
The calculation formula of (a) is as follows:
Figure BDA0003302548540000039
in the formula (I), the compound is shown in the specification,
Figure BDA00033025485400000310
in the k year
Figure BDA00033025485400000311
Sequence of meteorological index samples, alpha2And beta2Is an intercept term and a slope term of the linear regression model; epsilon2,kThe residual terms of the linear regression model.
By observing the precipitation okAnd forecasting the union of precipitation and meteorological indexes
Figure BDA00033025485400000312
Is determined by the regression equation
Figure BDA00033025485400000313
The calculation formula of (a) is as follows:
Figure BDA00033025485400000314
in the formula, alpha3Is the intercept term of a linear regression model, beta3,1And beta3,2Is the slope term of the linear regression model. Wherein the corresponding certainty factor can be obtained by comparing the sum of the squares of the residuals and observing the total variance of the precipitation.
And S3, respectively calculating the variance explained by the independently forecasted precipitation, the variance explained by the independently forecasted meteorological index and the variance repeatedly explained by the independently forecasted precipitation and the meteorological index based on set operation according to the certainty coefficient.
The expression formula of the variance explained by the individual forecasted precipitation is as follows:
Figure BDA0003302548540000041
the expression formula for the variance, interpreted by the weather indicator alone, is as follows:
Figure BDA0003302548540000042
the expression formula of the variance repeatedly explained by the forecast precipitation and meteorological indexes independently is as follows:
Figure BDA0003302548540000043
and S4, processing the variances by using a bootstrap method to obtain reference distributions of the three variances.
In this embodiment, the step of processing the variance by using a bootstrap method includes: and (3) disturbing the historical forecast precipitation data and the meteorological index sample sequence, and repeatedly executing the steps from S2 to S3 to obtain corresponding three variances until the preset iteration times are reached to obtain the reference distribution of the three variances.
In the present embodiment, the number of iterations is set to 1000.
And S5, comparing the original sample data with the reference distribution of the three variances to obtain a correlation result of the precipitation forecast capacity and the remote correlation action.
In this step, original sample data is compared with reference distributions of three variances by a single-side inspection method. Wherein, the step of comparing the original sample data with the reference distribution of the three variances comprises: selecting a significance level, typically 0.1, 0.05 and 0.01, corresponding to a reference distribution threshold of 90, 95 and 99 percentiles of the reference distribution, respectively; when the significance level is set to 0.1, an original sample data value is deemed significant if it is greater than the 90 th percentile of its reference distribution of corresponding variances, otherwise it is deemed insignificant. And then outputting the significance result as a result of the correlation between the rainfall forecast capacity and the remote correlation action.
In one implementation, there are 8 significant results, which are specifically shown in table 1 below.
TABLE 1 Association relationships represented by eight different combinations
Figure BDA0003302548540000044
Figure BDA0003302548540000051
Wherein, a notation of 1 indicates that the original sample data value is considered significant at the corresponding certainty factor, and a notation of 0 indicates that the original sample data value is considered insignificant at the corresponding certainty factor.
In the embodiment, the set operation is combined with the linear regression deterministic coefficient, and a bootstrap method and a unilateral test method are further combined, so that the overlapping and difference components in the observed rainfall information provided by the rainfall forecast and the meteorological factors are simply and effectively distinguished, and a reference is provided for the business use of the rainfall forecast.
Example 2
This example is based on the method for correlating precipitation forecast capacity with the remote correlation proposed in example 1.
The method takes the global season grid precipitation data of the United states climate forecasting center (CPC)1982-2010 as observation data, takes the second generation climate forecasting system CFSv2 of the United states environment forecasting center (NCEP) as forecast precipitation data, and takes the second generation climate forecasting system CFSv2 of the United states environment forecasting center as forecast precipitation data
Figure BDA00033025485400000612
The index indicates the ENSO phenomenon. Wherein, the CFSv2 forecast precipitation adopts 0 month forecast season precipitation. Take winter (December-January-February, DJF) as an example. The spatial resolution of observed precipitation and forecast precipitation is 1 degree multiplied by 1 degree.
As shown in FIG. 2, is DJF
Figure BDA0003302548540000061
And the distribution diagram of the indexes and the observed precipitation correlation coefficient. As can be seen from the figure, obvious remote correlation effects appear in many areas in the global range, but the effects are very different in different areas and show obvious spatial correlation. For example, in the south of north america,
Figure BDA0003302548540000062
the index is positively correlated with the precipitation in the region, the precipitation in the region is more in early-nino years, and the precipitation in the region is less in lanina years. In contrast, in the north of south america,
Figure BDA0003302548540000063
the indexes are in negative correlation with the precipitation in the area, which shows that the climate is dry in early nino and wet in lanina.
For the precipitation of each grid in FIG. 2, the observed precipitation and the forecast precipitation are established separately,
Figure BDA0003302548540000064
The indexes and the regression equation between the two union sets are respectively calculated to obtain corresponding certainty coefficients R2(o～f)，
Figure BDA0003302548540000065
And
Figure BDA0003302548540000066
as shown in fig. 3, are three deterministic coefficients R2(o～f)，
Figure BDA0003302548540000067
And
Figure BDA0003302548540000068
the global distribution of each. As can be seen from the graph, in some regions, the information provided by the forecast and the information provided by the forecast
Figure BDA0003302548540000069
The information provided is of comparable size and spatial distribution, with some overlap possible, e.g., in the south of north america, in the north of south america, in the east of africa, etc. In addition, the partial area forecast can provide more information, such as northern europe, northern asia, southeast australia, and so on. There is also a portion of the area,
Figure BDA00033025485400000610
more information may be provided, such as western australia. Overall, when the union of the two is used as an interpretation variable, the most information can be interpreted (i.e. the last row of subgraph in fig. 3).
For quantitatively forecasting precipitation
Figure BDA00033025485400000611
Respectively providing information and overlapped information, and further obtaining overlapped R by using a set operation method2And each independently R2. As shown in fig. 4, is the result of a collective operation, i.e.
Figure BDA0003302548540000071
Spatial distribution of the three variances. The distribution diagram shown in fig. 4 well distinguishes partial variances of the independent interpretation of the forecast precipitation, mainly in the northern part of the asian continent, the southeast part of australia, the west part of africa and the east part of africa. While
Figure BDA0003302548540000072
The information provided by the index is mainly distributed in the western Australia and the south Africa. Finally, the overlapping regions are mainly distributed in the south north america, the north south america, the south southeast america, the east africa, and parts of the south africa and east asia. The graphic results well confirm the expectation of fig. 3, which shows that the rainfall forecast capacity and the remote correlation effect correlation method provided by the invention can effectively distinguish forecast capacity and remote correlation effect
Figure BDA0003302548540000073
The indicators each provide information.
Further, the present embodiment applies to three sets of variances determined according to the deterministic coefficient
Figure BDA0003302548540000074
Figure BDA0003302548540000075
Significance tests were performed separately. There are eight different combinations of three significant results, as shown in table 1.
As shown in FIG. 5, for forecasting precipitation on the world grid
Figure BDA0003302548540000076
The incidence relation of the information classifies the situation distribution diagram, and displays the distribution of eight different situations on the space. The three digits in the legend correspond to the significance results given in Table 1, where the number 1 represents significance and the number 0 represents no significance, respectively, where the first digit represents
Figure BDA0003302548540000077
Of significance, second digit representation
Figure BDA0003302548540000078
Of significance, the third digit is
Figure BDA0003302548540000079
The significance of (a). The distribution map gives the final CFSv2 forecast precipitation sum
Figure BDA00033025485400000710
The difference and overlap of the respective provided information between the indices. For example, the "010" grid, i.e. forecasting precipitation and
Figure BDA00033025485400000711
the indicators both provide information on the observation of precipitation, and the information of both is overlapping. Such grids are distributed mainly in the south of north america, the north of south america, and the south of east americaEastern and southern africa, parts of east asia.
Further, as shown in fig. 6, the difference and overlap of the information are shown by the wien diagram. From the eight classification cases obtained, one grid was randomly drawn (grid positions are indicated in capital letters in the distribution diagram of FIG. 2), and the predicted precipitation for each grid were calculated
Figure BDA00033025485400000712
The information provided is represented by a wien diagram. R of forecast precipitation represented by a yellow dotted circle in the figure2I.e. R2(o-f), the gray solid line circles represent
Figure BDA00033025485400000713
R of index2I.e. by
Figure BDA00033025485400000714
The white part of the two overlapping is
Figure BDA00033025485400000715
The non-overlapped parts of the two are respectively
Figure BDA00033025485400000716
And
Figure BDA00033025485400000717
the total area of the three parts being
Figure BDA00033025485400000718
Figure BDA00033025485400000719
The Wien diagram of FIG. 6 is a good representation of the relationship between information, such as the D-grid (011), that the forecasting capability provides almost entirely
Figure BDA00033025485400000720
The information provided by the indicator is fully contained, indicating that on this grid,
Figure BDA00033025485400000721
the metrics can provide more information, while the predictive capability does not provide information beyond the far correlation. While the G grid (110) is reversed,
Figure BDA00033025485400000722
the information of the index is fully contained in the information provided by the forecast.
The experimental results show that the rainfall forecasting capacity and the remote correlation effect correlation method based on the certainty coefficient can effectively forecast rainfall and forecast rainfall
Figure BDA0003302548540000081
The difference and the overlap between the information provided by the indexes can intuitively show different incidence relation classification conditions, and can provide reference for the use of the forecasted business.
It should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.

Claims (10)

1. A rainfall forecast capacity and remote correlation action correlation method based on certainty coefficients is characterized by comprising the following steps:
s1, acquiring historical forecast precipitation data, observation precipitation data and meteorological index sample sequences to obtain original sample data;
s2, establishing regression equations of the observed precipitation, the forecast precipitation, the meteorological indexes and the union of the forecast precipitation and the meteorological indexes, and obtaining corresponding certainty coefficients through the regression equations respectively;
s3, respectively calculating the variance explained by the individually forecasted precipitation, the variance explained by the individually forecasted meteorological index and the variance repeatedly explained by the individually forecasted precipitation and the meteorological index based on set operation according to the certainty coefficient;
s4, processing the variances by using a bootstrap method to obtain reference distribution of the three variances;
and S5, comparing the original sample data with the reference distribution of the three variances to obtain a correlation result of the precipitation forecast capacity and the remote correlation action.
2. The method of claim 1, wherein the weather indicators included in the sequence of weather indicator samples comprise weather indicators
Figure FDA0003302548530000011
And/or
Figure FDA0003302548530000012
3. The method of claim 2, wherein the deterministic coefficient R is determined by regression equations of observed precipitation and forecasted precipitation2The calculation formula of (o to f) is as follows:
Figure FDA0003302548530000013
Figure FDA0003302548530000014
in the formula okRepresents observed precipitation data of the k year, fkThe forecast rainfall data of the kth year is represented, and K is the total year number of the rainfall data; alpha is alpha1And beta1Is an intercept term and a slope term of the linear regression model; epsilon1,kResidual terms of the linear regression model;
Figure FDA0003302548530000015
indicating the average observed precipitation over many years.
4. The method of claim 3, wherein the deterministic coefficient is determined by observing regression equations of precipitation versus meteorological parameters
Figure FDA0003302548530000016
The calculation formula of (a) is as follows:
Figure FDA0003302548530000021
in the formula (I), the compound is shown in the specification,
Figure FDA0003302548530000022
is a meteorological index of the k year, alpha2And beta2Is an intercept term and a slope term of the linear regression model; epsilon2,kThe residual terms of the linear regression model.
5. The method of claim 4, wherein the deterministic coefficient is determined by a regression equation of the union of observed precipitation and forecasted precipitation and meteorological parameters
Figure FDA0003302548530000023
The calculation formula of (a) is as follows:
Figure FDA0003302548530000024
in the formula, alpha3Is the intercept term of a linear regression model, beta3,1And beta3,2Is the slope term of the linear regression model.
6. The method of associating precipitation forecast capacity with remote correlation according to claim 5, wherein in step S3, the expression formula of the variance explained by forecast precipitation alone is as follows:
Figure FDA0003302548530000025
the expression formula for the variance, interpreted by the weather indicator alone, is as follows:
Figure FDA0003302548530000026
the expression formula of the variance repeatedly explained by the forecast precipitation and meteorological indexes independently is as follows:
Figure FDA0003302548530000027
7. the method for correlating precipitation forecast capacity with telemetry functions according to any one of claims 1-6, wherein the step of processing the variance by using a bootstrap method comprises: and (3) disturbing the historical forecast precipitation data and the meteorological index sample sequence, and repeatedly executing the steps from S2 to S3 to obtain corresponding three variances until the preset iteration times are reached to obtain the reference distribution of the three variances.
8. The method of claim 7, wherein in step S5, the original sample data is compared with the reference distribution of three variances by a single-edge test.
9. The method of claim 8, wherein the step of comparing the original sample data with the reference distribution of three variances in step S5 comprises: selecting a level of significance and determining a reference distribution threshold based on the selected level of significance; if the original sample data value is larger than the reference distribution threshold value of the corresponding variance, the original sample data value is determined to be significant, otherwise, the original sample data value is determined to be not significant; and then outputting the significance result as a result of the correlation between the rainfall forecast capacity and the remote correlation action.
10. The method of correlating precipitation forecast capabilities with telemetry-related actions according to claim 9, further comprising the steps of: and comparing the original sample data with the reference distribution of the three variances to obtain a significance result, and displaying the significance result through a chart.
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