CN111309778B - Climate mode evaluation and deviation correction method based on information entropy - Google Patents
Climate mode evaluation and deviation correction method based on information entropy Download PDFInfo
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Abstract
The invention discloses a climate mode evaluation and deviation correction method based on information entropy, which comprises the following steps: according to actual requirements, selecting a climate evaluation result and a climate measurement result of each climate model; calculating information entropy and mutual information of each climate model and the measurement result; obtaining VI and RVI diagrams; evaluating the merits of the climate model; selecting n weather evaluation models with better evaluation results to construct a multi-mode set forecasting system; the result correction is performed by the least square method. According to the invention, the output data of the multiple climate modes are taken as independent variables, the deviation correction model of the output data of the multiple climate modes is constructed, and the evaluation result is further corrected while the evaluation of the climate modes is realized, so that the accurate prediction of future climate situations is facilitated.
Description
Technical Field
The invention relates to the field of uncertainty evaluation methods of multi-climate mode output data, in particular to a climate mode evaluation and deviation correction method based on information entropy.
Background
The Yangtze river source region is used as an important component of the Qinghai-Tibet plateau of the main starting region and the regulating region of northern hemisphere climate change, has great influence on the ecological environment and social economic development of the eastern and southwest regions of China, and is one of the most special and fragile regions of the ecological system of China. Under the influence of global change, the climatic heating and drying trend of the Yangtze river source region is obvious, glaciers shrink, frozen soil is degraded, and lakes and beaches swamp type wetlands tend to be unwatered and developed. The ecological environment of the current river source area is facing the most serious worsening trend from the history, and has been paid unprecedented attention. In order to cope with possible changes in climate change, it is necessary to recognize the trend of these watershed climate changes, evaluate the climate change effect, and the primary condition is to obtain more detailed regional climate information.
Climate patterns are highly complex computer programs, a product of a combination of science and technology, a collective of human beings 'theoretical awareness of the systems behind them, that can be used to simulate or reproduce the vast majority of macroscopic features of the earth's climate. The climate pattern output data can be used for quantitatively estimating future climate change conditions, such as: the long-term prediction data of rainfall temperature and the like output by the mode become very important tools for recognizing, analyzing and evaluating the influence of climate change on water resources, ecological environment and the like.
Global climate system mode (GCM) is an important tool for climate simulation and future climate change scenario estimation, and is also the most viable tool. It can simulate high-rise atmospheric field, near-ground temperature and atmospheric circulation. In recent years, scientists in various countries use different global climate system modes to carry out a large number of simulation and prediction experiments, and a great deal of important results are obtained. Currently, the fifth coupling pattern comparison scheme (CMIP 5) includes up to 60 coupling patterns of 19 pattern groups, and the sixth coupling pattern comparison scheme (CMIP 6) may include more patterns. Due to the limitation of calculation conditions, the simulation of the regional climate and the climate change test by the GCM can generate larger deviation, and the regional climate situation is difficult to accurately predict. In addition, the estimated data output by different modes usually have non-negligible estimated errors, and the difference of the estimated effects among the modes is obvious, but the estimated data of each model can reflect certain local characteristics actually observed to a certain extent or at a certain level.
How to objectively and quantitatively evaluate and compare the performances of different climate modes, so as to realize accurate prediction of future climate situations is becoming more and more important. Currently, the commonly used climate pattern evaluation methods include a Portrait graph and a Taylor graph, wherein the Portrait graph is based on root mean square error, i.e. the Portrait graph only evaluates the root mean square error of each climate pattern. Therefore, this evaluation method has two disadvantages: (1) The correspondence between root mean square error and mode performance is not strictly monotonic, i.e. the decrease in root mean square error does not necessarily correspond to an increase in climate mode performance. (2) Although the root mean square error can be written as a function of the correlation coefficient and the standard deviation, i.e. the root mean square error contains both information of the correlation coefficient and the standard deviation, the magnitudes of the correlation coefficient and the standard deviation cannot be explicitly described by using the root mean square error alone, for example: the same root mean square error may correspond to completely different correlation coefficients and standard deviations. Furthermore, the Portrait plot cannot evaluate the overall simulation ability of multiple variables. The Taylor diagram can evaluate the simulation capability of a climate mode on a specific variable, and can evaluate the overall simulation capability of the mode on a plurality of variables. Meanwhile, the Taylor diagram can accurately display the correlation coefficient, the root mean square value and the root mean square error of each variable in each climate mode.
However, not all relationships can be interpreted in terms of variance and correlation. In many cases, the variables have a nonlinear dependence, a fact that cannot be correctly identified with a linear dependence. Furthermore, in the presence of outliers, the correlation between two variables may be low and the relationship between the two variables cannot be reflected with a correlation coefficient.
Accordingly, those skilled in the art are working to develop a method that can accurately evaluate climate patterns so that future climate scenarios can be accurately predicted.
Disclosure of Invention
In the theory of information, entropy is used to measure the expected value of the occurrence of a random variable. It represents the amount of information lost during signal transmission, also known as entropy, before being received.
Mutual information is a useful information measure in information theory, which can be seen as the amount of information contained in one random variable about another random variable, or as the uncertainty that one random variable has been reduced by knowing another random variable. Mutual information analysis has proven to be an effective method for comparing the relationship between clusters and studying time series, and has been successfully applied to information security and gene expression analysis. Many methods of estimating entropy and mutual information have been proposed, some of which rely on estimating potential probability density functions or estimating these quantities directly by fitting.
The invention provides a climate mode evaluation and deviation correction method based on information entropy, which adopts a new mutual information graph based on information theory instead of first-order and second-order statistics, and the position of the evaluation result of any model in the graph is determined by the information entropy and the mutual information of the model and reference distribution.
The mutual information graph based on the information theory adopted by the method comprises other types of relations between the two distributions so as to highlight the similarities and differences, and the mutual information graph can be identified through statistics and is mainly used for analyzing the similarities between the two distributions and the shared information between the two distributions. In particular, the mutual information map may represent edge entropy of two distributions, their mutual information, and a measure of the variation of their information over the probability distribution space. This mutual information map based on information theory has certain advantages over the previous Taylor map because it reveals a nonlinear relationship between the two distributions and is less sensitive to outliers (erroneous values) or partially corrupted or lost data. The information entropy-based climate mode assessment and deviation correction method provided by the invention is particularly used for comparing different climate assessment models by using the mutual information graph and carrying out sensitivity and uncertainty analysis on a plurality of variables in the models, so that the advantages and disadvantages of each climate assessment model are intuitively revealed, the output data of the climate mode is corrected, further future climate situations can be accurately predicted, and the method has important application value for improving the overall strength of the China for coping with climate change problems.
In order to achieve the above object, the present invention provides a climate pattern evaluation and deviation correction method based on information entropy, which is characterized by comprising the steps of:
step 1, selecting a climate evaluation result and a climate measurement result of each climate model according to actual requirements;
step 2, calculating information entropy and mutual information of each climate model and the measurement result;
step 3, obtaining VI and RVI diagrams;
step 4, evaluating the quality of the climate model;
step 5, selecting n weather evaluation models with good evaluation results to construct a multi-mode set forecasting system;
and 6, correcting the result by using a least square method.
Further, the information entropy in the step 2 is as follows:
wherein p (x) i ) For an event X in a reference distribution X i N is the number of events contained in the reference distribution X.
Further, the mutual information between the model Y and the reference distribution X in the step 2 is defined as:
where p (x, y) is the joint probability of the model and the reference distribution. P is p X (x) And p Y (Y) is the marginal probability of the reference distribution X and model Y, respectively.
Further, the VI graph in step 3 is a difference graph of information between the model and the reference distribution, where VI is defined as:
VI(X,Y)＝H(X)+H(Y)-2I(X；Y)
wherein H (X) and H (Y) are the information entropy of the reference distribution X and the model Y, respectively.
Further, the RVI profile of the step 3 is a normalized mutual information profile based on RVI, wherein
Wherein the RVI-based relationship measures normalized mutual information, which can be expressed specifically as:
further, the step 4 specifically includes:
step A, comparing different climate models by using a mutual information graph;
step B, performing sensitivity and uncertainty analysis on a plurality of variables in the model;
and C, revealing the merits of each climate evaluation model.
Further, the step 5 specifically includes linearly combining the extracted n climate modes to construct a multi-mode aggregate forecasting system
Z＝α 1 X 1 +α 2 X 2 +…α n X n
Wherein X is i (i= … n) climate data, α, for each of the n climate modes selected, including information on temperature, precipitation and humidity i (i= … n) are the scaling coefficients of the n climate patterns, respectively, which have a positive correlation with the preliminary evaluation results of the selected n climate patterns, lie between 0 and 1, and satisfy
Further, the step 6 specifically includes that the multi-mode set forecasting system Z in the step 5 judges the evaluation result by using the VI and the RVI graphs, and gradually adjusts the scaling factor so that the output result of the multi-mode set forecasting system is closest to the actual measured value. Specifically by least square method, i.e. the following least squares method
Where S is the actual climate measurement data.
Further, a plurality of climate simulation parameters are displayed simultaneously in the VI and RVI diagrams, including but not limited to: air temperature, humidity, air pressure and precipitation.
Further, the VI and RVI profiles are based on information theory.
The invention has the following advantages and beneficial effects:
1. the deviation of the evaluation result from the actual value of each climate mode is visually represented in a graph which retains certain metric properties.
2. The method can accurately evaluate the climate mode, so that future climate situations can be accurately predicted.
And the VI or RVI reveals that the parameter of the mutual information and the mode performance are strictly monotonic corresponding relation, namely, the reduction of the VI or RVI corresponds to the improvement of the mode performance, so that the observation is more visual.
The conception, specific structure, and technical effects of the present invention will be further described with reference to the accompanying drawings to fully understand the objects, features, and effects of the present invention.
Drawings
FIG. 1 is a flow chart of a preferred embodiment of the present invention;
FIG. 2 is a diagram of mutual information consisting of information entropy and information difference VI in accordance with a preferred embodiment of the present invention;
figure 3 is a RVI-based relationship for a preferred embodiment of the present invention.
Detailed Description
The following description of the preferred embodiments of the present invention refers to the accompanying drawings, which make the technical contents thereof more clear and easy to understand. The present invention may be embodied in many different forms of embodiments and the scope of the present invention is not limited to only the embodiments described herein.
FIG. 1 is a flow chart of a preferred embodiment of the present invention.
The embodiment provides a multi-climate mode assessment method based on information entropy, wherein output data of the multi-climate mode is taken as independent variables, a deviation correction model of the output data of the multi-climate mode is built, and the assessment result is further corrected while the climate mode assessment is realized, so that the method is beneficial to accurately predicting future climate situations. The method uses a new information theory-based mutual information graph instead of first-order and second-order statistics, and the position of the evaluation result of any one model in the graph is determined by the information entropy and the mutual information of the model and the reference distribution.
The specific steps of the embodiment are as follows:
step 1, selecting a climate evaluation result and a climate measurement result of each climate model according to actual requirements;
step 2, calculating information entropy and mutual information of each climate model and the measurement result;
step 3, obtaining VI and RVI diagrams;
step 4, evaluating the quality of the climate model;
step 5, selecting n weather evaluation models with good evaluation results to construct a multi-mode set forecasting system;
and 6, correcting the result by using a least square method.
The information entropy is as follows:
in the above formula, p (x) i ) For an event X in a reference distribution X i N is the number of events contained in the reference distribution X.
The mutual information between the model Y and the reference profile X is defined as:
in the above equation, p (x, y) is the joint probability of the model and the reference distribution. P is p X (x) And p Y (Y) is the marginal probability of the reference distribution X and model Y, respectively.
The information difference VI between the two distributions is defined as:
VI(X,Y)＝H(X)+H(Y)-2I(X；Y)
in the above formula, H (X) and H (Y) are information entropy of the reference distribution X and the model Y, respectively.
The mutual information diagram composed of information entropy and information difference VI is shown in FIG. 2, wherein c XY The definition is as follows:
in the above formula, H (X, Y) is the joint entropy of the model Y and the reference distribution X, and is determined by the information entropy of the model Y and the reference distribution X, and the mutual information between the model Y and the reference distribution X, which can be specifically expressed as:
H(X,Y)＝H(X)+H(Y)-I(X；Y)
in fig. 2, o is the position of the reference distribution X in the VI diagram, and · is the position of the model Y in the VI diagram. The position of the model Y in the VI graph is specifically determined by the information entropy of the model Y, the information difference VI, mutual information between the model Y and the reference distribution X, and the like.
VI-based graph measures a scaled mutual information SMI XY This can be expressed as:
in addition, each model can be displayed in the VI graph, and the distance VI between the model and the reference distribution X can reveal the advantages and disadvantages of the climate mode evaluation corresponding to the model, so that the future climate situation can be accurately predicted, and the method has important application value for improving the overall strength of the climate change problem of China. When the VI value is smaller, the simulation data representing the corresponding mode is better matched with the observation data, and the future climate situation can be better simulated.
At the same time, the VI graph can be simplified into a normalized mutual information graph in the following graph, wherein
Unlike VI-based graphs, RVI-based graphs measure normalized mutual information, which can be expressed in particular as:
fig. 3 shows a correlation diagram based on the RVI, and similarly, each model can be displayed in the RVI diagram, and the distance RVI between the model and the reference distribution X can also reveal the advantages and disadvantages of the climate mode evaluation corresponding to the model, so that the future climate situation can be accurately predicted, and the method has important application value for improving the overall strength of the climate change problem of China. Similarly, when the RVI value is smaller, the simulation data representing the corresponding mode is better matched with the observation data, and the future climate situation can be better simulated.
Furthermore, multiple climate simulation parameters may be displayed simultaneously in the VI and RVI maps, such as: air temperature, humidity, air pressure, precipitation, etc.
Specifically, the above method calculates p (x) using a nuclear density estimation method i ) For event X in reference distribution X i And p (x, y) is the joint probability of the model and the reference distribution.
After the preliminary evaluation process, the evaluation results of all the climate modes are ranked from high to low, and n climate modes with better estimated results are selected from the evaluation results to carry out deviation correction. Specifically, the extracted n climate modes are linearly combined to construct a multi-mode aggregate forecasting system
Z＝α 1 X 1 +α 2 X 2 +…α n X n
Wherein X is i (i= … n) climate data, α, for each of the n climate modes selected, including information on temperature, precipitation and humidity i (i= … n) are the scaling coefficients of the n climate patterns, respectively, which have a positive correlation with the preliminary evaluation results of the selected n climate patterns, lie between 0 and 1, and satisfy
The evaluation result is judged by adopting the VI and RVI diagrams in the invention, and the scaling factor is gradually adjusted so that the output result of the multi-mode set forecasting system is closest to the actual measured value. Specifically by least square method, i.e. the following least squares method
In the above formula, S is actual climate measurement data. And finding an optimal set of proportionality coefficients according to the calculation result, thereby realizing deviation correction, optimizing the output result of the climate mode and accurately evaluating the climate scene.
The foregoing describes in detail preferred embodiments of the present invention. It should be understood that numerous modifications and variations can be made in accordance with the concepts of the invention without requiring creative effort by one of ordinary skill in the art. Therefore, all technical solutions which can be obtained by logic analysis, reasoning or limited experiments based on the prior art by the person skilled in the art according to the inventive concept shall be within the scope of protection defined by the claims.
Claims (8)
1. A climate pattern evaluation and deviation correction method based on information entropy, comprising the steps of:
step 1, selecting a climate evaluation result and a climate measurement result of each climate model according to actual requirements;
step 2, calculating information entropy and mutual information of each climate model and the measurement result;
step 3, obtaining VI and RVI patterns,
the VI map is a map of information differences between the model and the reference distribution, where VI is defined as:
VI(X,Y)＝H(X)+H(Y)-2I(X；Y)
wherein H (X) and H (Y) are the information entropy of the reference distribution X and the model Y respectively,
the RVI map is an RVI based normalized mutual information map, wherein,
wherein the RVI-based relationship graph measures normalized mutual information, specifically expressed as:
step 4, evaluating the quality of the climate model;
step 5, selecting n weather evaluation models with good evaluation results to construct a multi-mode set forecasting system;
and 6, correcting the result by using a least square method.
2. The method for evaluating and correcting deviation of climate pattern based on information entropy according to claim 1, wherein in step 2, the information entropy is:
wherein p (x) i ) For an event X in a reference distribution X i N is the number of events contained in the reference distribution X.
3. The method for evaluating and correcting the deviation of the climate pattern based on the information entropy according to claim 1, wherein in the step 2, the mutual information between the model Y and the reference distribution X is defined as:
wherein p (x, y) is the joint probability of the model and the reference distribution, p X (x) And p Y (Y) is the marginal probability of the reference distribution X and model Y, respectively.
4. The method for evaluating and correcting the climate pattern based on the information entropy according to claim 1, wherein the step 4 specifically comprises:
step A, comparing different climate models by using a mutual information graph;
step B, performing sensitivity and uncertainty analysis on a plurality of variables in the model;
and C, revealing the merits of each climate evaluation model.
5. The method for evaluating and correcting deviation of climate patterns based on information entropy according to claim 1, wherein the step 5 comprises the steps of constructing a multi-mode set prediction system by linearly combining the extracted n climate patterns
Z＝α 1 X 1 +α 2 X 2 +…α n X n
Wherein X is i (i= … n) climate data, α, for each of the n climate modes selected, including information on temperature, precipitation and humidity i (i= … n) are the scaling coefficients of the n climate patterns, respectively, which have a positive correlation with the preliminary evaluation results of the selected n climate patterns, lie between 0 and 1, and satisfy
6. The information entropy-based climate pattern evaluation and deviation correction method according to claim 1, wherein the step 6 specifically comprises determining the evaluation result by the multi-mode aggregate forecast system Z according to the step 5 using the VI and RVI maps, and gradually adjusting the scaling factor so that the output result of the multi-mode aggregate forecast system is closest to the actual measured value. Specifically by least square method, i.e. the following least squares method
Where S is the actual climate measurement data.
7. The information entropy based climate pattern evaluation and deviation correction method according to claim 1, wherein the VI and RVI graphs simultaneously display a plurality of climate simulation parameters, comprising: air temperature, humidity, air pressure and precipitation.
8. The information entropy based climate pattern assessment and bias correction method according to claim 1, wherein the VI and RVI maps are information theory based.
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| CN109186774A (en) * | 2018-08-30 | 2019-01-11 | 清华大学 | Surface temperature information acquisition method, device, computer equipment and storage medium |
| CN109636660A (en) * | 2018-10-22 | 2019-04-16 | 广东精点数据科技股份有限公司 | A kind of agricultural weather data redundancy removing method and system based on comentropy |
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