CN110020409A - Surface air temperature Structural Observed data Analysis method based on self-adaptive kernel density estimation algorithm - Google Patents
Surface air temperature Structural Observed data Analysis method based on self-adaptive kernel density estimation algorithm Download PDFInfo
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Abstract
The present invention relates to a kind of surface air temperature Structural Observed data Analysis methods based on self-adaptive kernel density estimation algorithm, belong to surface air temperature Structural Observed data Analysis field, this method introduces adaptive algorithm on traditional fixation window width Density Estimator algorithm squeezes out, adaptation coefficient is introduced in window width, capableing of brought by the sparse degree of effecting reaction sample observations influences, then adaptive algorithm is improved again, window width is replaced with into optimal bandwidth, making surface air temperature observe the result obtained under data to meet all mean square errors is minimum, so that improved adaptive approach is completely suitable for surface air temperature observational data.
Description
Technical field
The present invention relates to surface air temperature Structural Observed data Analysis fields, have especially invented a kind of improved Density Estimator algorithm
Surface air temperature element is analyzed.
Background technique
In recent years, the trend of global warming is more obvious, and temperature change brings serious influence to society, therefore obtains
The extensive concern of scholars has obtained many significant conclusions as research.For China, to geographical location spy
Such as plateau, the basin research of different area is more, achieves many achievements, and the relatively stable southeast of temperature is studied not
Foot.Traditional air temperature analysis method majority, which is established on the basis of time series, predicts and analyzes following variation tendency, in sky
Between in angle various countries experts and scholars also carried out a series of research, but the factor for influencing temperature change is extremely complex, and deposits
In apparent regional and seasonal variation.Existing research is insufficient to analyzing the reason of causing temperature change.
Summary of the invention
In order to solve the problems in the existing technology the present invention, provides a kind of for surface air temperature Structural Observed data Analysis
Method.
In order to achieve the above object, technical solution proposed by the present invention are as follows: one kind is based on self-adaptive kernel density estimation algorithm
Surface air temperature Structural Observed data Analysis method, include the following steps:
Station data sample in step 1, a period of time sequence of selection objective area surface air temperature observational data, i-th
A station data is Xi=(xi1,xi2,…xij,…,xin)T；
Step 2, according to Density Estimator formulaCalculate Density Estimator value；Wherein K (x)
For kernel function, h is window width, hiFor the i-th corresponding window width of website, n is sample size；
Step 3, design window width coefficientThen adaptive window width is hi *=λihi, will freely adapt to window
Window width in width replacement Density Estimator formula, obtains self-adaptive kernel density estimation formula
Wherein g isArithmetic average；α is sensitive parameter, meets 0≤α≤1；
Step 4, design optimal bandwidthOptimal bandwidth is substituted into the window in self-adaptive kernel density estimation formula
Width obtains
Wherein, c is parameter,For the standard deviation of station data sample.
Be further designed to above-mentioned technical proposal: the kernel function uses Gaussian function.
Parameter c and α is chosen respectively using the particle swarm algorithm of adjustment, then optimal bandwidth formula adjusts in step 4
Are as follows:Obtain improved self-adaptive kernel density estimation formula:
Wherein, ω and μ is parameter, and value range is respectively between [- 0.5,0.5] and [- 0.1,0.5].
Parameter c and α initial value design are 1.06 and 0.2.
The present invention is generated compared with the prior art to be had the beneficial effect that
Self-adaptive kernel density estimation algorithm either precision or fitting degree of the invention is all than traditional fixation window width
Algorithm is good, and in addition algorithm proposed by the present invention all has good precision of prediction and fitting degree under multiple dimensioned, and tradition is calculated
Method can only be applied under small scale.
From principal level, the variation for understanding each region under the variation characteristic and Multiple Time Scales of temperature is special
Point facilitates the deep understanding to Calculating Temperature Variation and its influence factor, it is therefore desirable to dissect surface air temperature observational data
The attributes such as the frequency, numerical values recited, trend and the influence of weather, position for temperature under Multiple Time Scales, and then can be deep
Enter and is analyzed and studied.The statistics that algorithm proposed by the present invention can be very good to analyze China's surface air temperature observational data is special
Property, it provides fundamental basis for further research surface air temperature observational data.
Method proposed by the present invention can effectively analyze the statistical property of surface air temperature observational data, and influence on it
Reason can also be further analyzed, therefore can be effectively applied to the analysis and application of surface air temperature observational data.
Detailed description of the invention
Fig. 1 is flow chart of the embodiment of the present invention；
Fig. 2 a is the MAE Contrast on effect column diagram of the Density Estimator algorithm of the method for the present invention and the fixed window width of tradition；
Fig. 2 b is the RMSE Contrast on effect column diagram of the Density Estimator algorithm of the method for the present invention and the fixed window width of tradition；
Fig. 2 c is the NSC Contrast on effect column diagram of the Density Estimator algorithm of the method for the present invention and the fixed window width of tradition；
Fig. 2 d is the IOA Contrast on effect column diagram of the Density Estimator algorithm of the method for the present invention and the fixed window width of tradition；
Fig. 2 e is the MAE Contrast on effect line chart of the Density Estimator algorithm of the method for the present invention and the fixed window width of tradition；
Fig. 2 f is the RMSE Contrast on effect line chart of the Density Estimator algorithm of the method for the present invention and the fixed window width of tradition；
Fig. 2 g is the NSC Contrast on effect line chart of the Density Estimator algorithm of the method for the present invention and the fixed window width of tradition；
Fig. 2 h is the IOA Contrast on effect line chart of the Density Estimator algorithm of the method for the present invention and the fixed window width of tradition；
Fig. 3 a is Density Estimator algorithm test result figure of the method for the present invention in Xuzhou website；
Fig. 3 b is Density Estimator algorithm test result figure of the method for the present invention in Suqian website；
Fig. 3 c is Density Estimator algorithm test result figure of the method for the present invention in Lianyun Harbour website；
Fig. 3 d is Density Estimator algorithm test result figure of the method for the present invention in Huaian website；
Fig. 3 e is Density Estimator algorithm test result figure of the method for the present invention in Yangzhou website；
Fig. 3 f is Density Estimator algorithm test result figure of the method for the present invention in Nanjing website；
Fig. 3 g is Density Estimator algorithm test result figure of the method for the present invention in Zhenjiang website；
Fig. 3 h is Density Estimator algorithm test result figure of the method for the present invention in Changzhou website；
Fig. 3 i is Density Estimator algorithm test result figure of the method for the present invention in Yancheng website；
Fig. 3 j is Density Estimator algorithm test result figure of the method for the present invention in Wuxi website；
Fig. 3 k is Density Estimator algorithm test result figure of the method for the present invention in Suzhou website；
Fig. 3 l is Density Estimator algorithm test result figure of the method for the present invention in Nantong website；
Fig. 4 is 12 website distribution map of Jiangsu Province.
Specific embodiment
With reference to the accompanying drawing and specific embodiment the present invention is described in detail.
According to the flow chart of present invention method, as shown in Figure 1, first having to acquire required website in certain time sequence
Then air temperature data in column carries out basic pretreatment to data, then, carry out different Density Estimator tests respectively,
It is evaluated using different evaluation indexes, test and the progress of 12 website of Jiangsu Province is finally carried out using algorithm proposed in this paper
Analysis.
It below will be to Jiangsu Province Xuzhou (station number: 58027), Suqian (station number: 58131), Lianyun Harbour (station number: 58044), Huaihe River
Peace (station number: 58141), Yangzhou (station number: 58245), Nanjing (station number: 58238), Zhenjiang (station number: 58248), Changzhou (station number:
58343), Yancheng (station number: 58154), Wuxi (station number: 58354), Suzhou (station number: 58349), Nantong (station number: 58259) altogether
1988 to 2007 days of 12 websites, night, season average air temperature value are counted as observational data and carries out embodiment analysis, further
Illustrate the present invention:
Comparative example one
Choose 12, Jiangsu Province website surface air temperature observational data, 1988 to 2007 six hour datas of temperature and the moon
Average data pre-processes the data obtained above, preprocessed data as observational data are as follows: take wherein 08 when with 14 when
The average value of temperature takes the 1-3 month for the first quarter as day samming with the average value of temperature when 02 when taking 20 as night samming,
The 4-6 month is the second quarter, and the 7-9 month is the third season, and the 10-12 month is fourth quarter, obtains corresponding time series X=(X1,
X2,…,X12), wherein i-th of station data is Xi=(xi1,xi2,…xij,…,xin)T。
It is tested using traditional Density Estimator algorithm of fixed window width, according to the formula of Density EstimatorIt is calculated, wherein K (x) is kernel function, and h > 0 is window width, and fixed value is generally chosen
1.8~2, n are sample size.
Choose the preferable Gaussian kernel function of mathematical property:As kernel function.
Based on the thought of least square error (LSCV), according to integrated square error (MISE) minimum, derivation finds out optimal
Fixed window width, specific reasoning process are as follows: according to integrated square error formulaWherein deviation formula isVarianceThe further abbreviation of deviation formula can be obtained:AndIts deviation and variance substitution integral is square
Error formulaWherein, k2=∫ x2K(x)
Dx is enabledIf necessary to MISE minimum, then AMISE reaches
Minimum finds out optimal bandwidth h so asking first derivative that it is enabled to be equal to 0 AMIS.The optimal bandwidth h derived are as follows:After kernel function is determined as Gaussian kernel, it can be derived from:WhereinFor the standard deviation of sample.
Comparative example two
Window width used by comparative example one is fixed window width, can not effecting reaction sample observations sparse degree institute
Bring influences, this comparative example joined adaptive algorithm on the basis of comparative example one.
The Density Estimator value obtained according to comparative example oneIn hiWithOn the basis of proportional, pass through
Design window width coefficientIt improves, wherein g isArithmetic average: i.e.α is spirit
Quick parameter meets 0≤α≤1, and effect is best when α is 0.5 in practical application, therefore adaptive window width is hi *=λihi, replacement pair
H in ratio onei, self-adaptive kernel density estimation can be acquiredBut the above method is applied directly to surface air temperature sight
It is in survey analysis and improper, wherein initial h lacks a selection criteria, pass through the selection method for substituting into optimal bandwidth, needle
Different websites are chosen with different initial window width hi, combining adaptive parameter obtains suitable for the adaptive of surface air temperature observational data
Answer Density Estimator formula:
Embodiment
It is not able to satisfy all mean square errors by the result that the algorithm of comparative example two is obtained in the case where surface air temperature observes data
It is minimum, illustrates that this method is not properly suited for surface air temperature observational data, it is therefore desirable to redefine the choosing of optimal bandwidth
Method is taken, the present embodiment proposes optimization method are as follows: new window width formula is provided based on optimal bandwidth formula:Wherein c
It is variable with a parameter, in order to enable the Density Estimator curve graph obtained is close to data truth, is sought using intelligence
Excellent algorithm determines parameter c and a therein, so that RMSE value is the smaller the better, improved formula are as follows:
Wherein n is sample size, and K (x) is Gaussian kernel,For adaptive window width coefficient, parameter c
It is undetermined with α.The present embodiment uses the particle swarm algorithm of adjustment to choose respectively to parameter c and α: being with Density Estimator function
Objective function, it is assumed that a N-dimensional space, the particle populations X=(X being made of the temperature record of multiple websites1,X2,…,Xd),
In i-th of particle data Xi=(xi1,xi2,…xij,…,xin)TPass through objective functionIt calculates it can be concluded that cuclear density is estimated
One group of potential solution of meter:It is with root-mean-square error RMSE again
Fitness function, wherein parameter c and α is referring to the optimal bandwidth in fixed window width algorithm in initial solutionSet, be 1.06 and 0.2, by the speed V of traditional PS O be adjusted to dual changed factor ω and
μ, position X are adjusted to window widthThen its formula adjusts are as follows:Parameter ω and μ scope limitation are existed simultaneously
Between [- 0.5,0.5] and [- 0.1,0.5], improved self-adaptive kernel density estimation formula is obtained by above method:
The present embodiment is more preferable for the fitting degree of truthful data, can show the trend of data itself.
As shown in Fig. 2, choosing four common evaluation parameters: mean absolute error (MAE), is received root-mean-square error (RMSE)
Assorted coefficient (NSC) and coincident indicator (IOA) are described in fixed window width, optimal fixed window width and improved adaptive window width
Under test effect:
Wherein, n is sample points,For i-th j Density Estimator value, y (xij) it is i-th j initial data frequency
The mean value of each histogram of rate histogram,For frequency histogram mean value.
As shown in figure 3, improved Density Estimator algorithm is carried out applied to 12 station surface air temperature observational data of Jiangsu Province
Test, and binding site (shown in Fig. 4) and climate characteristic to its test result map analysis and are summarized.
The test effect of above-mentioned three kinds of algorithms illustrates in precision and intends under index MAE, RMSE, NSC and IOA comparison
Application of the fixed window width algorithm of tradition in terms of Jiangsu Province's surface air temperature observational data season temperature and improper in conjunction degree, and
Self-adaptive kernel density estimation algorithm either precision or fitting degree after improvement is all preferable.It has furthermore been found that of the invention
Precision and fitting effect of the algorithm that embodiment proposes under multiple dimensioned are all optimal, and the fixed window width of tradition in comparative example one
Algorithm can be only applied to the test of small scale data, and to sum up method proposed in this paper is with regard to precision and fitting aspect in multi-site and more
There is effect excellent enough under scale compared to conventional method.
The impact factor of climate characteristic is greater than position feature, and under season scale, the more past south in position, whole samming is got over
Height, temperature change is more stable, and the spring and autumn samming represented with 15 DEG C lengthens, and the adjustment effect of ocean compensates for position to a certain extent
Setting bring by north influences；Under day and night scale, to 20 DEG C -30 DEG C representative summer, the variation tendency of climatic effect samming,
Position then influences the duration of samming, and marine climate and monsoon weather bring influence difference are little in weather, ocean
Adjust the size and duration that can improve samming；To the spring and autumn represented with 10 DEG C -20 DEG C, closer to the southeastern coastal areas, day and night
Difference is bigger between samming curve；To with the winter of 0 DEG C of -10 DEG C of representative, northwesterly is got in position, and the samming duration at night is longer and begins
Be higher than day samming eventually, it is possible thereby to find under scale in different times, weather and position to the influence mode of temperature change with
Capability of influence is different from, therefore facilitates going deep into for follow-up study in influence of the analysis different characteristic to temperature.
Method of the invention is not limited to the various embodiments described above, and all technical solutions obtained using equivalent replacement mode are fallen
Within the scope of the claimed invention.
Claims (4)
1. the surface air temperature Structural Observed data Analysis method based on self-adaptive kernel density estimation algorithm, which is characterized in that including as follows
Step:
Station data sample in step 1, a period of time sequence of selection objective area surface air temperature observational data, i-th of station
Point data is Xi=(xi1,xi2,…xij,…,xin)T；
Step 2, according to Density Estimator formulaCalculate Density Estimator value；Wherein K (x) is core
Function, h are window width, hiFor the i-th corresponding window width of website, n is sample size；
Step 3, design window width coefficientThen adaptive window width is hi *=λihi, replaced window width is freely adapted to
The window width in Density Estimator formula is changed, self-adaptive kernel density estimation formula is obtained
Wherein g isArithmetic average；α is sensitive parameter, meets 0≤α≤1；
Step 4, design optimal bandwidthOptimal bandwidth is substituted into the window width in self-adaptive kernel density estimation formula, is obtained
It arrives
Wherein, c is parameter,For the standard deviation of station data sample.
2. according to claim 1 based on the surface air temperature Structural Observed data Analysis method of self-adaptive kernel density estimation algorithm,
Be characterized in that: the kernel function uses Gaussian function,
3. according to claim 2 based on the surface air temperature Structural Observed data Analysis method of self-adaptive kernel density estimation algorithm,
It is characterized in that: parameter c and α being chosen respectively using the particle swarm algorithm of adjustment, then optimal bandwidth formula adjusts in step 4
Are as follows:Obtain improved self-adaptive kernel density estimation formula:
Wherein, ω and μ is parameter, and value range is respectively between [- 0.5,0.5] and [- 0.1,0.5].
4. according to claim 3 based on the surface air temperature Structural Observed data Analysis method of self-adaptive kernel density estimation algorithm,
Be characterized in that: parameter c is 1.06 and 0.2 with α initial value design.
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